Yes you can have your domain at one registar and hosting can be at any provider.
It's allways safe to keep those 2 separate , just to keep you out of trouble.
It's as easy as it gets, you register a domain and the hosting company provides you the nameserver which you need to modify at the domain registar.
I dont know what you mean by full control of the domain, if you buy it at a registar you own the domain for the prepaid period of your choice.
If you register it at a hosting company they might enter their details at the domain ownership, i'll suggest you read the TOS before buying a domain from a web host, if unclear just drop a mail to the sales department.
I would also like to add, that some web hosts require you to stay with them for web hosting after you buy the domain from them. ex. 1and1.com
So just be sure you ask the sales department prior to purchase to be sure that there wont be any trouble. I also would like to suggest a registar like godaddy.com, where you can buy a domain from them and host you site elsewhere. They also provide excellent support for you and your domain.
By no means are you limited to them though, many times you can find much better rate from other registars.
There is no lifetime subscriptions to regular TLD's like .com .net .info etc...
You can prepay for as much as 10 years, and ofcourse you can renew your subscription, but you can only prepay for 10 years tops.
Regarding the change of host that's not a big problem regarding the domain, you simply change the namerservers to point to your new web host
You can only register a domain name for a maximum of 10 years.
But as darkstorm said, the preferred way is to register your domain with a good registar (I prefer ICANN accredited ones, not resellers) and host the web site elsewhere. You can then change web hosts anytime you like and just change the DNS addresses at the domain registar.
While I can't say this is authoritative, many people here register the domain name
with the registrar and the website hosting with the hosting company separately.
If one's "compromised" for whatever reason, at least the other won't necessarily
Between the two, the domain name account is arguably more important. Because
if you lose that (knock on wood), you'll really have a hard time getting it back...
...if ever at all.
I've seen many a domain name account compromised, and not all were resolved to
the customer's benefit. It can get that ugly, I assure you.
And by registering your domain name with an actual registrar, you'll have a whole
lot more control to it than with a reseller.
Your title here says it best:
Can one register a domain name with and take hosting else where?
YES, and thats what is advisable to do.
1. Select a registrar. Purchase domain name first.
2. Select web host. Purchase hosting account and you will receive your welcome email with your account information. This will contain your host DNS info and all you will need to do is go back to the registrar...login to update your nameserver info supplied by your host.
Its all very easy to do and once you've done it once you'll be a pro.
I would recommend godaddy to register the name ONLY and then find your webhost!