Learn English – Difference between “related to” and “associated with”

In the case of (2) and (4), these are OK and have about the same meaning.

In the case of (1) and (3), you can't really say this with "meeting" alone.

But this usage could be used to start a list of items. For example:

In order to make the cake, begin/start with the cake flour, then add the butter and eggs.

Though maybe if you are working on an agenda:

We need to start with the meeting, then go to the production line.

In general (AmE), I think the usage of start and begin are about the same, though in some contexts one may be a more commonly used than the other.

In 5 minutes we will start the race.

'to' is directed towards only one person, whereas, 'with' includes both people. Example: John was talking to Smith. John was speaking with Smith. In the first sentence, only John is speaking. In the second sentence, a conversation of two people is implied.