Translation:After the third hour we go to the forum.
The Roman day was divided between 12 hours of daylight and 12 hours of night. So in the summer, daylight hours were longer than they were in the winter, and the reverse was true for the night hours (it also meant that hours were different lengths in different parts of the empire). Counting hours started from dawn and then again at dusk, so this is the third hour after dawn (or dusk).
No, AD never takes dative. It may take either accusative or ablative, the latter of which is identical in second-declension words like forum.
- AD + ablative -> at a place (ad forum sumus "we are at the forum")
- AD + accusative -> towards a place (ad forum imus "we go to the forum")
A few other prepositions have the same characteristic (notably in and, slightly differently, super.) In any case, in this phrase, since you are moving toward the forum, then it must be AD + accusative.