Normal for derailleur to make noises? I have a giant anyroad 1 2015.  It has this as components
Crankset    Shimano Tiagra, 34/50
Cassette    Shimano Tiagra 11x34, 10-speed

That is 7 cogs in the cassette, and 2 cogs on the crankset.

Is it normal for the derailleur to make noise when the chain is on the smallest cogs? It also happens a bit when the front derailleur is on the smallest cog, and the rear one is on the second-smallest.

Yes - I understand you're not supposed to do this - your chain should try not to twist. My question is this - is this normal? Or is it just a poorly installed/adjusted derailleur?  My rationale is that it should be 'silent' on any combination of gears since the bike was built to do this.
Is the question is it normal for a it to make noise when cross-chaining from smallest to smallest which you're not suppose to do?  Yes, but by doing so you are putting more stress on the chain and cogs, it is bad for your drive train and can result in dropping a chain or mucking up your gears faster than normal.

It is likely making noise because it is rubber or grinding on the derailleur or chain set.

The bike was not made to do that, you said yourself that you know you are not suppose to do it. 

"My car sounds like crap when i run it with zero oil in the engine.. is this normal?"