Irish non resident Uae where to apply for a visa for China

hello I cancelled my work visa in UAE but I'm still here on tourist type. as Irish person can I apply one for China in Abu Dhabi or do I have to go back to Ireland to apply?
The reason I'm free to go there is because my contract here has finished but I would rather travel from Uae because it's shorter than from Ireland.
I want to go to Beijing and go to Mongolia then back to china for about three weeks and exit from Hong Kong. Does that mean a multiple entry one or double entry?
finally i am worried about flight booking before getting it issued. I don't have an invitation from China. I would just be booking in a youth hostel for the first two nights before planning holiday after that. Would that be enough to get the tourist L for China?
Thanks Thomas.