Their policy said no refunds, but Kevin did mention they will consider case by case. As far as downtime guarantees go, most companies have a policy of issuing credit for downtime, not refunds for downtime.
Yeah, and most of those credit policies are worthless. For example, a company might say "We guarantee 99.99% uptime and will give you a prorated credit if we exceed this!". That might sound great until you do the math.
If you assume 30days * 24hours * 60mins in a month (43,200 minutes), that only allows for 4.32 minutes of downtime to meet the 99.99% uptime guarantee. Let's say a box is down for 8 hours - that obviously is bad and exceeds the guarantee by 475.68 minutes. But when you look at the proration credit, it's worthless. Since you only paid $3.33/month for this VPS, the fact that they had 1.11% of downtime means you would get a credit for about $0.04. This doesn't just go for CVPS - in fact I don't think they have a published credit for downtime policy - it's just a standard BS policy amongst all providers. Unless you have a high level contract with set SLAs and penalties for failing to deliver on them, the provider doesn't have to pay you squat. Hell, even if you were paying $100/month for a server, that would only equate to a little over $1 in credit.
Your domain doesn't show up automatically if you change the name servers. You still have to setup your VPS with LAMP if it wasn't already done then add DNS records to your VPS for your domain.
LAMP has nothing to do with DNS resolution. First, you don't even need the MP part of LAMP unless your site requires PHP and/or MySQL - Apache can work just fine on it's own to host a basic site. But if your DNS is configured correctly, the IP should still resolve even if none of that is running.
However, DNS changes are not instantaneous. When you change a domain's NS record, it can take hours (or more) for it to fully propagate. Even A/MX/etc. records on the same NS server can take a while if they were cached by other DNS servers.