Your use of present tense is fine. The first sentence starts with present tense in the first clause and then uses present perfect in the second. That's perfectly ok and that sentence is good.
The second sentence is all present and that's fine too. I would suggest a few changes to the second sentence though. "a very serious problem FOR me" sounds better. Also the three clauses in the sentence don't work well together. They need to be split up and some connecting words would help them flow better. Here is are some possibilities.
I usually sleep very late. Insomnia is a serious problem for me, and I need to solve it.
I usually sleep very late because Insomnia is a serious problem for me that I need to solve.
I usually sleep very late because Insomnia is a serious problem for me; I need to solve it.
I'm not a great writer, I'm sure someone else could do better.
The two very's also sound redundant. It would be better to change one of them to a synonym, or just take out the one before serious since that already provides emphasis.