linking two websites together

First decide what's the real purpose of having the two connected via links. If you are selling at one site then handling the transaction at the other, then you have no option but to link the two together.

There's nothing wrong with this kind of 'reciprocal' linking arrangement as far as google is concerned, given that each of the two websites has different content.

If you wanted to create an SEO benefit from having two sites, then you would link from one to the other but not back again - so a one-way link rather than two-way or reciprocal.
You could dig deeper into the subject if this is a marketing model that you want to develop with other sites linking via one-way links to the target site. If that's the case then you need to create a physical disconnect between the link hosts and the link target. This is done usually by registering private domain features (protected whois) and by using a dedicated IP address for the host/target sites.

That should get you started at least.

I see no problem with it. It's not going to make a big difference one way or the other because if both of your sites are brand new, you won't be pushing much link power from either one. You won't be penalized for it, so don't worry about that. You might actually want to consider combining the two ideas and just making one site out of it.

I wouldn't worry about linking your sites together like that. Google is more worried about things like trying to send millions of backlinks to a website in a single day etc.