I decided to dedicate 10 minutes every day to five finger exercises. The book I use is Schmitt Op. 16 (free on imslp).
There are a lot of them, should I keep doing the first one for a few weeks until I have it at a desired speed (108?) and then progress to the next one?
Or should I go through the book without a metronome?
If you practise just one of them "for a few weeks" you will die of boredom long before you finish the exercises!
There a groups of exercises that are similar, e.g. 1-33, 34-64, 65-110, etc.
You could split 34-64 into subgroups depending which finger is held down.
Start by practising all the first group at the same speed - don't rush through the "easy" ones and slow down for the "hard" ones. When you are to making progress with those, start on the next group, and then work on both groups together.
You will probably find that working on the one groups improves the others at the same time.
Yes, but it depends
If you want to strenghten your fingers, and improve, elasticity and precision is always better to play them how they was written. If you want, always using the metronome, you could even try to go a little faster (not over-doing it) to improve even more, but don't spend months on every single one.
If one is too difficult, and it takes too long to practice, just try doing your best, and don't aim for perfection.
