1. I agree with Brian25. The most likely cause of your front derailleur issue is that your shift lever doesn't have enough friction to hold against the derailleur spring pressure. Usually that type of friction shifter has a screw on the side that needs to be tightened.

2. It looks to me like your chain was sized using the commonly recommended big/big method. That method will yield the shortest chain that will safely cover your big/big combination. The way that your rear derailleur looks when in that combination is normal