you are using the stellar shared hosting plan from name cheap ?
Yes, the stellar one ! i bought it at $19 a year , the last year , & renewal price was about $38, now they reduced the price as you mentioned !
I've only run alidropship sites on that hosting & so far no compatibility problem, yes they have all the system requirements to run alidropship plugin.
As for SSL, they include a free one with their package, & it's COMODO, and they have an automated tool to help you set it up at one click ! i'm using it along with other SSL's i bought outside Namecheap.