Over the last two weeks, I have faced two peculiar issues with accessing my website from normal broadband connections.

1st issue:
I was able to browse all the sites from my home ISP, except for my website and other two famous e-commerce sites in India. When I switched to other ISPs, the sites were working fine. After contacting the ISP, they changed the Primary and Secondary DNS records on the modem and then I was able to browse all the sites normally.
My site + the 2 sites was accessible only when the ISP changed its DNS record on the modem. The thing common between the three sites (including ours) which were not accessible was that our nameservers point to GoDaddy's domaincontrol.com.

2nd issue:
All the sites were loading well, except for my website where 5 out of 10 pages failed to load when browsing normally. This issue was on the two Windows 7 systems using a particular ISP in my office. All other systems running Windows XP and all other ISPs were resolving to the site normally. And today, a day after I reported the issue to the ISP, I am able to access my site normally without any issues. Maybe the ISP did some DNS refresh or something. I can also see that the bounce rate on our online marketing campaigns suddenly dropped which had increased on the last 2-3 days.
Again seems to be an issue where the ISP 'may not have been able to resolve to our IP / DNS properly'.

I am not a technical person nor have much knowledge about DNS stuff. However, as commom sense, somewhere it seems to be an issue with DNS somewhere. We run online campaigns and we are a consumer internet site. So, if such things happen, it can directly effect our site traffic.

Questions I am seeking answers to:
1. Why was only our site at the problem's end and all other sites were working fine in issue 1 and issue 2. This zeroes in the problem to our site specifically with single ISP while the site was all fine on same ISP in different locations?
2. In the first issue, if the ISP DNS was the problem, why was only our site not accessible (along with the other 2)?
3. Do you suspect this could be because of using GoDaddy for hosting DNS records. (We use the default DNS manager where the domain name is hosted to point the records to our Amazon EC2 server).
4. Do you suggest we go for an alternative DNS hosting account where no matter if the problem is with ISP, the traffic to our site is not affected?