When do I use speech marks and do I use " or ' ?

I understand the basic concept of speech marks:

"Hello," said Mike.
"Hi!" replied Sam. "It is such a lovely day."

but what about when I am writing about a name of something or a company? Would I write:

I walked by Isaac's Ice-cream Parlour. or:

I walked by "Isaac's Ice-cream Parlour". or:

I walked by "Isaac's Ice-cream Parlour." or:

I walked by 'Isaac's Ice-cream Parlour'. or:

I walked by 'Isaac's Ice-cream Parlour.'

As you can see it is all confusing me. There are a lot of options. It might not even matter!

Also I do understand that ' is an apostrophe:

That is Sarah's pen.

The pen is Sarah's.

but I have seen it used for speech marks too.

Also, (and sorry this question is getting quite long) what if I need to put speech marks around normal words. I know that seems silly but I mean like if you speak you might make quotation marks with your fingers when saying a word or phrase like:

The punishment was supposed to "improve our behaviour".

Here, the person saying this does not think the punishment improved their behaviour in any way. Also, whoever gave the punishment said it would improve their behaviour.

What if someone is saying it:

"The punishment was supposed to "improve our behaviour"" said Mary.

or:

"The punishment was supposed to 'improve our behaviour'" said Mary.

or:

"The punishment was supposed to 'improve our behaviour'," said Mary.

Sorry if I wrote this in a confusing way, but I am very confused too!

Thank you for bothering to read this very long question and thanks in advance for the answers!