Not an easy question to answer. Where did this list of units come from?
I suspect a Swedish source. There is another, different, list of the unit here – link again from Swedish sources.
Unfortunately the Russian sources don't agree with this list! More on this later.
Your List:
Troizki is probably another spelling of Troitsky, or at least that is the most likely. But the unit with this name wasn't called this until later on and according to the Russians was not in Poland. It is possible that this was a unit from this area if your list is correct.
Inglis: This unit later became the Vyborg regiment. It was garrisoning Narva according to the Russians.
Patkul: This unit was certainly at the battle and survived to fight later in the war, indeed it was quite a high status unit. It was later called 'Rentzel's' or the 'Saxon' regiment. It was not 'named' (given a 'regional' name & I don't know what happened to it after Peter the Great's time). The number of battalions is uncertain.
Repnin's Grenadiers: The Russians are not supposed to have grenadier battalions at this time but there is some evidence that they did. Most likely this means (if the unit really existed) that the unit is an ad hoc formation formed for the battle.
Gulitz: This unit also was almost certainly at the battle. It was disbanded after the battle & the remaining men put into Patkul's/Rentzel's unit above.
Arnstedt: No information.
Belling: Possibly the Siberian regiment. The location of this regiment is uncertain. More likely these last 2 units are as Gulitz above.
What the Russians say:
So the above would be my best bet if the Swedish sources are correct. Unfortunately I don't think they are, or at least they are not helpful.
The Russian units at Fraustadt were part of a low quality Corps sent to help the Saxons/Poles some years before. So it is very unlikely that units that would be 'named' would be there. There was also a lot more than 10 battalions available in this group but they had been campaigning for some time. Finally 9 units (7 'Line' and 2 Streltsy) were disbanded after the battle & the remaining people put into Patkul/Rentzel's unit, 6 of these are identified by the Russians as being there. Many other units were also disbanded after the battle but not put into another unit. These include at least 1 unit that the Russians say was at the battle but didn't go to Rentzel's unit.
We therefore have lots of possibilities. Maybe the 'battalions' were composite battalions made up of a number of real, but by this time small, battalions. Maybe the battalions were Patkul/Rentzel's plus the 9 units added to this unit. Maybe it was a combination of the 2. Maybe Patkul/Rentzel's had 2 battalions and there was a combined grenadier unit of some kind – with the balance being made up of the 7 units the Russians say were there or some other combination.
For various complicated reasons I have my best guess, but it is a guess. But I am 99% sure that the units at the battle, except for Patkul/Rentzel's, were never 'named' & indeed were disbanded after the battle.