Is that possible to host in one service and keep the domain in another registrar. Will that be even a wise idea?
Keep everything in different places as much as possible. As a newbie, you can start from keeping domain, hosting and nameservers in different locations.
So, which registrar will be good? I mean in terms of security and money?
If you have only 1 domain, pick the one with low renewal fee and good reputation. I would pick namesilo.
While going on with the process as I can see in every registrar, the WHOIS have to be disabled and what nots!! Will my site be down at some point? Even for a brief period?
You can migrate your websites from server A to server B with zero downtime.
First of all, do not start from changing your nameservers unless you will actually migrate your website to your new hosting after 48 hours or later. That 48 hours vary based on the domain extension of your website. At the time of this writing, it's 48 hours for dot "com" and "net" extensions, 24 hours for "org" and "info" extensions.
1- Drop TTL values of your current DNS records (particularly A records and CNAME if exists -avoid having CNAME in DNS-) to a minimum possible value like 300 (5 minutes). The new TTL value will not be live until the time of the old TTL value has passed. In other words, if the old TTL was 6 hours for an A record before you lowered it to 5 minutes, the changes in that A record will not be fully active before 6 hours.
2- Upload website files to your new hosting, create a new database and import database backup, edit config file to connect new mysql and edit .htaccess and other important hosting files if necessary.
3- Change the DNS records (A record IP, MX, TXT and so on) and raise their TTL values to an optimal value.
4- Then change nameservers only if you think the new nameservers are better. Otherwise never change your nameservers. Just change DNS records. Grab DNS records of your new hosting and add those new records to your DNS. That's it.
As to your problem with WHOIS, if you try to transfer a domain with private whois, registrar should normally forward the emails to you. If not, it's a bad registrar. They might either not forward emails or might try to discourage you from transferring your domain to another registrar. Private whois is not needed to be disabled as long as you receive the emails sent to the registrant email address in your private whois.
I am an experienced webmaster. When I have free time I can answer all questions regarding to hosting and webmaster related things. I can even give you cpanel accounts (not from EIG). I used the hosting services mentioned above then moved to unmanaged servers to host my websites. I used knownhost managed VPS for longer than a year. They didn't have shared hosting in those years. They were good. Godaddy shared hosting was indeed good hosting, had excellent uptime. It was only difficult to use for newbies in the years with their own custom control panel. For my websites, I rented shared, managed VPS, unmanaged VPS, dedicated servers from 20+ different providers over the last 15 years. I can't comment on hosting support quality for any hosting as didn't need to contact support except to inform them about the problems only they can fix. Frankly most hosting services I used so far were good for the price I paid. The real major difference is the expertise level of the users. Yes there are some really bad hosting companies but they are rare. Small hosting companies are usually better in technical quality. If you omit human factor in a hosting, such as support quality, hosting quality is only hardware and network quality. Because hosting is a computer, is a machine that makes your websites files online. If you know how to use that computer space then you don't need their support staff. If their service is frequently functioning bad, then you are free to move to another hosting without contacting them. Just another reason for not to change your nameservers or not to use the nameservers of the given by hosting.
