Your testing tells the story.
The Server your Hosting account is on is slow. Doubt things will improve so best to start looking for another Hoster.
As to questions in general for a Hoster, start making a list of questions that are important to you. Then keep a list of potential Hosters in Spreadsheet format, easier to track why you like or don't like, someone's Service. Once you have a shortlist of about 5 names you start getting serious. Contact them by eMail, phone, whatever, and ask a few questions about their packages. That should give who to start with now and who to immediately move to, if plan B is required. And don't lose that list!
With any potential Hoster, Features / Price / Support can be checked out before signing up. The last point to consider, Service or Uptime, cannot usually be determined until one actually starts using it or, unless the Hoster has a link to their Uptime stats.
To help overcome that, there are various places that provide Free or Paid uptime monitoring and the following three provide both:
http://easymonitor.com/
http://siteuptime.com/
http://host-tracker.com/
Using a combination of all on one Hoster or each on different Hosters, can give you a good idea on their Service before using them.
Overall, research and patience are two important tools when checking most things, Hosting or otherwise. ;)
The learning is in the doing.
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