I would like to know if somebody has/had problems with hosting a bitcoin project on NameCheap.
Not really an issue in regards to bitcoin project being hosted there but have in mind that they don't offer their services to several countries (I wasn't allowed to purchase domain and hosting there and I suggest you to get in touch with their support first).
And if yes, do you know good and also same priced alternatives?
I never had issues with SteadyTurtle:
https://steadyturtle.com/web-hosting.phpForum thread:
https://bitcointalk.org/index.php?topic=972575.0
Their a bit pricier (for the first year) but when it comes to the second year for renewal (in comparison with NameCheap), their a lot cheaper:
1st year with one time 30% discount = $4.165/month for ultimate plan
1st year (same with renewal for the next years) with recurring 20% discount = $4.76/month for ultimate plan