A lot of hosting providers will let you host multiple domains I use a shared server and have 4 blogs and 6 websites on the same server, you add them as addon domains in your hosting cpanel

Once you have registered your domain you will just need to point the name servers to your hosting provider, I recommend imageleet.com as an hosting provider I have used them for over 10 years and support is second to none, they also give you access to softaculous which installs wordpress for you automatically what ever domain you choose

When registering your domains you can opt out of whois but it does give you more credibility if you are listed

When purchasing your domain names make sure the domain provider lets you change name servers some don't like you to do that as they like you to host with them.

I recommend daily.co.uk or 123reg.co.uk they both allow your to change name servers.

I hope this helps

Depends on how much time and money you have. I have around 50 different blogs. I have six tier 1 blogs (unique c-class hosting), try and buy aged domains from go daddy. Then I have 50 free blogs pointing to the 5 blogs (tier 2). All my blogs are word press so I can use article builders posting function. Then I use magic submitter to build 2.0 back links to tier 3. Then use magic submitter to back link into the 2.0 sites. End out come is pr 2-3 blogs with high end moz ranks.

1. you can use seo hosting which most people are against or you can different accounts from different hosting providers which is safer but is more expensive and takes more time to setup

2. Domains can be under one registrar as long as you have private whois on each of them

That's okay for a small blog network.

If you have a large network or multiple small ones, I recommend that you have different hosting providers. In other words, I wouldn't put all my eggs in one basket. For instance, having all your sites on a 100 IP hosting package is risky IMO.

Having a separate shared hosting account for each domain is the safest, but this can get expensive.

You should be fine as long as you stick with multiple smaller SEO hosting packages on different accounts and thru different providers.

Yes, that is fine. You just need to have private registration and unique nameservers.