Is 請 also mean "to treat" in Mandarin? I answered a question about the character 請,  http://www.cantonese.sheik.co.uk/phorum/read.php?14,137964,137965#msg-137965 on other site.

In Cantonese, 請 can mean: "to treat; to pay for someone" beside the listed meanings of " to invite" in the dictionary on that site. 

I suddenly realized it may not be the case in Mandarin, I think I heard Mandarin say: 「這頓飯我作東」, 「這頓飯我來付」，but do Mandarin say 「這頓飯我來請」 or  「我今晚請吃晚飯」？
Yes.

These phrases 『这顿饭我来请』『今天我请客』『我请』 very common in Mandarin.