It appears that "quaesitum" and "ad inquirendum" are legal terms. See, for instance, this text, which repeats the following phrase multiple times:
tam quaesitum quam ad inquirendum
Another example of this usage is found in Histoire générale de Languedoc, which is also the record of a donation of land:
Propterera cedimus . . . quantumcumque in ipsam curtem visi sumus habere et possidere totum et ab integrum ibi cedimus cum domibus aedificiis et apertinentiis cum boscis et vineis terris cultis et incultis, omnia et ex omnibus quaesitum et ad inquirendum divisum et ad dividendum quantumcumque ibi de Rainone et de Oddonbetto adquisivimus totum et ab integrum ei perpetualiter ad possidendum pro peccatis nostris minuendis supradictis sanctis exorantibus ...
The above example is especially relevant because it makes it abundantly that the two are meant to be understood as correlates.
It turns out that "ad inquirendum" carries over into contemporary legal terminology. See the definition given in Ballantine's Law Dictionary:
A writ commanding an inquiry or investigation.
In other words, it seems roughly similar to an "inquest": a legal inquiry into (in this case) the inventory of forfeited possessions.
"Quaesitum," we recall, is the past participle of "quaero," which is the root word of "inquiro." Judging from the fact that "quaesitum et ad inquirendum" is paired with "divisum et ad dividendum," I feel confident translating "quaesitum et ad inquirendum" as follows:
...into which an inquiry has been made and shall be made...
A full translation of the long and convoluted sentence ("Has itaque res...quidquid elegerint.") would thus be:
Therefore, we grant these items, along with their possessions, houses, buildings, cultivated and uncultivated lands, woods, fields, pastures, waters or waterways, neighboring through-ways [?], exits and regresses, into which an inquiry has been made and shall be made, or whatever amount of the preceding things were in the possession of this same Rato and which came or ought to have come to us and is of our right and possession in the matter of property, whole and entire, without restriction [cf. in exquisitum], as the perpetual possession of this same monastery, so that whatever the caretakers and servants of the above-mentioned monastery should wish to do or judge by ecclesiastical right concerning the previous items and properties, they may through this free concession of our authority have the power to do whatever they choose.
