+0
Can I say,
(a)The dog swam across / at / on / over / in /
into the river two hours ago.
+0
across, in, into - these are correct with different meanings. Try looking up their meanings in a dictionary.

At and on are incorrect.
Comments  
Students: Are you brave enough to let our tutors analyse your pronunciation?
If I saw a dog swimming on the way to other place, I think I can use " across". When should I use " swam in" or " swarm into"? What kind of situation?
No.

Across - to go from one side of something to the other. He walked across the road. (He was on the pavement one side of the road and crossed over to the pavement on the other side of the road.

In and into can be confusing sometimes. In this context:

In. 1 a -- used as a function word to indicate inclusion, location, or position within limits <in the lake> <wounded in the leg> <in the summer>

Into. 1 -- used as a function word to indicate entry, introduction, insertion, superposition, or inclusion <came into the house> <enter into an alliance>.

So, the dog swims in the river means that the dog is swimming and the location is the river. The dog swims into the river means that the dog is swimming, and enters the river. It was already swimming. Perhaps it was swimming in a lake and then turned off into the river?
Vincent TeoCan I say,
(a)The dog swam across / at / on / over / in /
into the river two hours ago.
Hi Vincent,

Adding to Nona's comments, I'd like to pitch in my 2 cents

We can't arbitrarily insert a prep. into a sentence which has flexible meanings. The example you gave was just that.

I saw a dog swimming across the river- fine. This means it was in the water, swimming it's way toward the other side of the river bank.

I saw a dog swimming in the river. also fine, but it only means you saw a dog in the water swimming, however, with no direction as to which way it was going.

I was a body of a dead dog floating on the river. - Fine, This means the dog was lifelessly drifting with the river current.
Students: We have free audio pronunciation exercises.