You're correct that 使って is "use(d) and". if you need to translate sentences very faithfully like legal documents, the corresponding combinations of English and Japanese sentences would be as follows:
the pen I used and wrote sentences with
the pen I used to write sentences with
Practically, however, there is little difference between these two, and this degree of deviation in translation is usually acceptable. For a learner who has acquired the basic grammar, it's important to learn to not worry about something like this too much.
Some may be wondering how this ところの is working:
These are actually correct and natural Japanese phrases, but at the same time, they are quite stilted and literary, and that's why Google Translate failed to translate them naturally (the natural version is shown at the beginning of my answer). A beginner should probably revisit this pattern much later after becoming able to solve JLPT N1-level problems.
Anyway, this type of ところの is something that is only sometimes inserted to emphasize (?) a relative clause:
the action he took
the present I gave to her
the person who passed this street yesterday
the restaurant where you can see the ocean
the time when the sun rises
The versions with ところの sound stilted, pompous, and politician-like to me, but there is no difference in meaning. This construction works especially well when the noun that has been pulled out is the object of the verb, as in your examples. In other types of relative clauses, like the ones I marked with
?, ところの sounds less natural, but they are not unheard of.
EDIT: Here is another way in which ところの can be used naturally. The basic meaning of the phrase doesn't change with or without ところの, but I feel that ところの makes the modifying clause a little more reserved or euphemistic.
the theory of relativity as I understand it
the "Paradise," as that philosopher calls it
the gods as believed in by the Japanese people