Problem number 1 isn't a problem, it's a first gear thing and it happens to pretty much every manual. I've had it happen to every single manual transmission car I've owned, and I had it happen all the time when test driving cars when I was a mechanic. You can do one of the following to get it into first:
1. Shift into another gear and then first.
2. Leave it in neutral, release the clutch and press it again, then put it in first.
3. In the off chance the first two don't work, put it in second and let the clutch out just a tiny bit then press it again and shift into first.
It happens in the first place because the synchros aren't lined up and doing one of the three things above helps get them lined up. Do not jam it, though, that can cause damage.
For problem 2, as others said, it could be a poorly adjusted linkage or it it could be an internal issue. If your car is still under warranty I'd suggest taking it in for a look first rather than doing it yourself. This will get it on the books and if the problem worsens after your warranty expires it'll give you a leg to stand on for getting it fixed anyway. If you don't have a warranty anymore, then yeah, try that adjustment guide and see what happens.