These are interesting uses, but too powerful for a cantrip
Both of these uses require the recipient to have encode thoughts as well
It's odd that you say you learned this as an additional means of communication, because the spell itself says:
Casting this spell while holding a thought strand allows you to instantly receive whatever memory, idea, or message the thought strand contains. (Casting detect thoughts on the strand has the same effect.)
That is the only way to receive the encoded thoughts - so if you want to transfer your knowledge of flute playing, the recipient will need one of the two spells as well. If you want to lay a trap for someone, you are limiting your targets to those who already have one of the spells.
The spell is limited to a single memory
As the spell says (emphases mine):
You pull a memory, an idea, or a message from your mind
A single memory is not much to work with. In some cases, a single memory might be very impactful - the identity of the killer, knowledge of what the passcode is on a magical trap, etc. But a single memory of playing a flute would not impart knowledge of 'how to play' a flute. At best, a single memory might be of one flute lesson, or one practice session. Granted to someone who doesn't play the flute, it would impart as much ability as...a single actual lesson for that person would, or perhaps less if it was not the first lesson and thus built on a foundation they did not have.
But wait! you might say. What if I encode multiple memories and pass them all off in succession? It is a cantrip, so I can just produce hundreds of memories at the cost of six seconds each, and the person receiving all of them would eventually learn, no?
No. Because the spell also says the strand:
persists for the duration or until you cast this spell again
So you can't make more than one of these strands at a time, since making a second one would destroy the first. Now, it doesn't say that casting the spell again removes the memory from someone that has already accessed it, so I suppose you could cast the spell repeatedly and hand the strands off to someone who read them as fast as you cast them, one at a time. But if you are both there, in contact with one another, why not just teach them how to play the flute? I can think of a few niche cases, but as a pre-recorded mass transfer of knowledge, that is beyond the power of the spell.
Similarly, if the person receiving the strand can only read it by casting the spell themselves, one memory at a time, they are hardly going to be overwhelmed by a trapped flood of memories. And 'trying to pull all your memories into a single strand' is again beyond the power of the spell, as written.
But you could make a spell like this
As a DM, you can homebrew spells, and as a player character, you can research new spells, and your ideas sound like interesting concepts to develop, but at higher levels than a cantrip. This stack has a 'homebrew review' tag if you would like to pitch a spell concept (I would suggest one at a time) and would like help refining it or gauging an appropriate power level.
You might also want to review the cantrip guidance, which provides a +d4 bonus to a single skill check. Depending on the level of the recipient, a +d4 might be about equal to their proficiency bonus. However, since the bonus lasts for the shortest of one check, or one minute, or concentration, it seems less powerful than what you are proposing. Since guidance is a cantrip, your more powerful 'grant proficiency in one skill for some time' spell would need to be higher.
Now contrast your idea with the spell enhance ability. As a second level spell with concentration, it permits the recipient to have advantage on all skill checks for a given attribute. Since advantage is roughly equivalent to +5, having it on all skill checks for one attribute is clearly more powerful than granting proficiency on a single kind of skill check or tool use check. Thus, what you are proposing - a spell that grants proficiency in a single skill or tool - might be first level if it required concentration or second level if it did not.
The second effect - melting someone's brain from an overload of memories - seems similar in effect and power to spells like synaptic static, symbol (Pain), symbol (Stunning), power word pain, and power word stun. If this is the kind of effect you are after, the spell level should be somewhere between 5th and 8th depending on the details - but certainly not a cantrip!
