1) There must be backup tire in the trunk. Normally, in the States we would say: There must be a spare* in the truck. Spare is the same as backup, but in the context of a car, everyone would know it's a tire, so you can omit tire if you say spare. 2) You should do your homework ahead of time if you want to get a good grade. Perfect 3) He felt down with regard to his favorite comic shop was closing down. Felt down is more informal where as with regard to is formal language. So I would suggest taking out the formal phrase with regard to and use because. Informal: He felt down because his favorite comic shop was closing down 4) Firstly, I thought that this program is too difficult but it seems to me I'm gradually getting hang of it. At first, I thought this program was too difficult, but it seems to me I'm gradually getting the hang of it (now). 5) I ate quite a few pancakes for lunch and thereby had stomachache. Thereby is too formal and doesn't fit naturally in this sentence. Instead: I ate quite a few pancakes for lunch and got a stomachache. I ate quite a few pancakes for lunch and then had a stomachache. I ate quite a few pancakes for lunch. As a result, I got (or had) a stomachache.