'Making' suggests the idea of 'creating' : for example, you make a pizza, make a suggestion, make a noise, make a mess, and so on.
'Doing' means performing or carrying out a job: for example, you do an exam, do exercises, do your work.
This is just a general guide. There are also lots of idiomatic expressions, such as 'do your best', which you just have to learn.
As for 'take' and 'have', in many cases they are interchangeable. For example, you can say 'take a shower' or 'have a shower'. The expressions with 'take' are more common in American English, and those with 'have' are more common in British English, but the meaning is the same.
Hope that helps. And yes, that's a really cute baby you've got there.