My room mates have these models - HP DV5 1104TU (or TX, need to check) & Dell Studio 15 (with ATI 256 MB). So, I may be able to answer some of your questions.
1. Any specific problems with these models? Like heating issues with HP laptops
No problems observed with either so far. HP was bought 1 week ago. Dell was bought about one month ago.
2. In terms of looks which one is better?
In my opinion, HP looks much better. (I have a DV5 1105tx.)
3. After sales service and customer care
I am very impressed with HP customer care. When I bought my DV5 1105tx, there was a free Wii Music receiver with it. It was not delivered even after the specified time. So, I wrote to customer care. A lady wrote to me back from her personal HP email id (unlike other customer care where the mail will be from
customercare@company.com, the replies to which will go to some other person and not the originally handled person). She cc'd the email to the agency responsible for delivering the goods giving them directions on what needs to be done. I got the device after 10 days. After 15 days, this lady once again wrote to me asking whether I received the gift. Having really bad experiences with customer cares of many (worst being Sony Ericsson), I was very much surprised by the response from HP.
4. Free Goodies J
In addition to the 950 Rs. gift voucher offered by the HP dealer, there was a home theatre system worth 5000 Rs (I think) with DV5 1104tx. Dell Studio 15 came with Creative ep630 ear buds.
5. Battery Backup
Not sure how much. If they let me check, I will post here.
6. Performance
If you require, I can post benchmark results for these 2.