No it is not. In Spanish -ito -ita works that way but in English, there is no such thing.

I'd say no. In general, the diminutive is not used as much in English as much as in Spanish. You could say, "little hut" or even "cute little hut." Hope that helps!

If you mean 'hot' and 'hotty' then yes, although I wouldn't say it expressed tenderness... A hut is a small house.