Learn English – the difference in usage between “for instance” and “for example”

Influence has two main connotations that affect doesn't. The first is that of relation to process rather than state, so that something might affect a rock but rarely would circumstances arise where we could speak of that rock being influenced. The second, and weaker, connotation is of emotive response being involved; this is probably the connotation that makes it feel less appropriate to use in reference to a bike's performance. (We do speak of mechanistic processes being influenced, though, especially complex ones.)

At least to me, 'topic' and 'subject' refer to something more specific than 'theme'.

For example, I might say, "the topic of discussion will be.." but I would never say "the theme of discussion will be..".

In this example, saying 'theme' feels wrong because it's impossible to decide what the 'theme' was before the discussion occurs. But we can decide what the topic will be.

But afterwards you might say "the general theme was that we should blabla..". 'Theme' generally refers to the dominant/unifying idea behind something. You might talk about themes when discussing literature etc.