Let me list the option:
a) Narrow-cast thought sending
b) Broadcast thought to any intelligent creature within defined range
c) Specialized telepathy to a specific creature (no penalty but have not learned it)
d) Generalized telepathy (will face penalty but have learned it but not test it)
e) Broadcast to specific creature within defined range
Your abbreviated labels are not entirely clear to me, so I'm going to respond to them.
a) Narrowcasting, to my mind, always means sending a message to an individual mind; it is the norm for most telepathic skills. You read the mind of a single target; you can send thoughts to the mind of a specific target; you can connect in a two-way connection with a single target; you can place thoughts in the mind of a single target. That is all narrowcasting, most like the use of a telephone.
b) Broadcasting is the unusual form, in which a signal is sent out to all minds. Because broadcasting is the unusual form, I usually take it as "all sentient minds within a specified physical distance range". It need not mean that. For most skills, you could have a "broadcast" version that reached "all sprites within range" or "all butterflies within range". You could have such skills which reached "all minds familiar to me, wherever they are". You could divide minds into categories of any sort for which you can defend these as a category of minds.
c) For most telepathic skills, such as mind reading, thought projection, and those which implant thoughts into another mind, there is a table of penalties--you are best at contacting minds that are exactly like your own (such as a temporal duplicate or a divergent self in another world, or even when you are using telepathic skills on yourself), and then (the normal level) those whose minds are akin to yours--called human minds, but in your case specifically sprites (I will not say whether humans or elves are covered under this for you at present). When you move away from your own "kind", you move toward humanoid minds--other intelligent creatures whose minds are a bit different from yours--and animal minds--creatures whose intellect puts them below the level of what you would ordinarily recognize as thought--and alien minds--intelligent beings that are of similar intellect but entirely different mind structures. For most telepathic skills, those categories are penalized, progressively more.
The quirk hits with telepathy. The trick with telepathy is that if you want to connect to other "human" minds like Lelach and Morani, you use a telepathic skill that is particular to such minds. If you want to communicate with humanoid minds (whatever they happen to be in any particular universe), there is no penalty, but it does require the use of a different skill, one of a slightly higher bias rating, because it is not so easy to attune your mind to theirs. Telepathy to animals (which includes plants, as long as you are in a world in which plants have minds) is yet another skill, and telepathy to aliens is yet another.
This means that for you to open a two-way telepathic link between your mind and that of a butterfly, you would need to learn telepathy to animals; but once you do so, that same skill will work for communicating with mice, bears, even (in this world, at least) trees and grass. There is no penalty for such two-way communication, but you have to have the right skill to do it.
(This is why I said you would have to roll for that.)
d) Most of my comments on point C should clarify the concept of generalized telepathy, unless by "generalized" you mean "broadcast", in which case the points under B will cover that.
e) "Broadcast to specific creature" makes no sense, given those definitions, unless you mean "broadcast to specific creature type", which would mean developing a telepathic link to "all butterflies". I would expect such a skill to be geographically limited, mostly because if you were to connect to all the butterflies in the entire universe it would probably blow your circuits pretty quickly. After all, they're known to burst into the most outrageously inane songs about unicorns for no apparent reason....
More practically, I can easily envision a skill that enables you to send thoughts to multiple targets, and one that enables you to hear all the thoughts in a specified limited area, but a skill that enables you to create a two-way communications network between multiple minds on a single roll is at best unlikely.
With that clarified, let's focus on one skill at a time. What, exactly, do you want to attempt to do telepathically?
*****
You succeed in reading the neural patterns in your hand, projected as a distinct phantom limb, such that you can "feel" how you make your hand do what it does.
You fail in your attempt to read your mother's hand, but it seems simply to be that it's a new skill and you're not that good at any of your skills yet, particularly the first few times you try to use them. There is every reason to think that you now know how to read the neural patterns in someone's actions.
*****
The problems with tagging plants are partly that you have a much more limited selection to attempt to tag and partly that they are so much more difficult to read even than animals, which are considerably more difficult to read than sprites. Yes, over time you can expect to have more plants tagged, but it's slow going.
*****
Your wings wrap forward around your arms; you instinctively tuck your arms inside when rolling over the wing on that side, and you can push yourself over with the wing in much the same way you would with an arm.
The joints in the wings are very limited but numerous, such that it curves very smoothly, as perhaps a thin sheet of metal might, without noticeable bend points--more like a butterfly than a bird, but more flexible than a butterfly.
*****
Over the course of a few weeks you manage to become specifically able to identify hair and saliva from yourself (you are still drooling and having trouble controlling this), your mother, and your father. You don't have as much contact with the hair and saliva of other creatures, other than the mice that are sometimes cooked for dinner, and the saliva is generally gone by the time you see them, and the hair soon after.
*****
Lelach is intent on having you learn English before you learn Spritish. It appears that when you are older you will be taught to read and write Spritish, but your parents think that it is not a language spoken outside of school. Thus they discourage your grandparents from speaking it around you, and they do not speak it themselves.
*****
I have stats for a six-month old; with this post you are not quite six months--you are in your fifth month. However, your stamina is above average for your age, as is your strength. On the other hand, you are pushing yourself hard, and often exhausted. We'll have to look at your practice sessions closely.
In fact, that's a good idea--in anticipation of your six month anniversary, give me list of how you have been using your practice slots since birth and what changes you would like to make if you are able. We'll get your stats up, adjust them for your practice, and get your new practice session in place next time.
*****
--M. J. Young