miscellaneous questions

1. No need for a comma and "that" is correct since it clarifies the bill we are talking about. It is the bill that was passed Tuesday, not another bill.
2. Either way is fine.

https://proofreadmyessay.co.uk/writing-tips/word-choice-that-vs-which/

To explain the difference between ‘that’ and ‘which’, we need to look at restrictive and non-restrictive relative clauses.

Restrictive and Non-Restrictive Relative Clauses
A restrictive relative clause restricts the meaning of what we’re saying. For example:

The house that I built survived the storm.

In this case, ‘that I built’ is restrictive because it specifies the particular house we’re talking about. This implies that we’re specifying one house out of several possible houses.

A non-restrictive clause, on the other hand, simply provides more information:

The house, which I built, survived the storm.

In this case, the relative clause ‘which I built’ is set apart with commas. This shows that it isn’t essential to the main part of the sentence. We use non-restrictive clauses if there is no doubt about what we’re discussing but want to provide extra detail.

In summary: restrictive clauses cannot be removed from a sentence without changing its meaning, while non-restrictive clauses are additional detail and set apart with commas.

That or Which?
You may have noticed that we use ‘that’ for a restrictive clause and ‘which’ for a non-restrictive clause in the examples above. This is the standard usage in American English.

In British English, however, ‘that’ and ‘which’ can both be used for restrictive clauses. But in both the US and the UK, non-restrictive clauses are only written with ‘which’.

If you want to avoid confusion, it makes sense to use ‘that’ for restrictive clauses and ‘which’ for non-restrictive clauses. But this is a matter of style when it comes to restrictive clauses, especially in the UK. Keep the following in mind if you’re unsure:

That or Which?

Example Sentence

British English

American English

That (Restrictive)

The house that I built survived.

✓

✓

That (Non-Restrictive)

The house, that I built, survived.

✗

✗

Which (Restrictive)

The house which I built survived.

✓

✗

Which (Non-Restrictive)

The house, which I built, survived.

✓

✓

Thanks, engineer.

Many thanks, Miss Toad.