If someone starts work half way through the year and makes out-of-paycheck contributions to their HSA account that amount to less than $3,450 (say they amount to $1,450), would they be able to deposit the remaining amount ($2,000) from a checking account to the HSA account? If yes, would they be able to deduct the remaining amount ($2,000) against their salary income when they file taxes during tax season?
Yes, you can contribute the remaining amount, up to your contribution limit, into your HSA directly from your checking account.
When a contribution that is sent in by your employer, whether the employer has paid for it or it has been deducted from your paycheck, that contribution is removed from the income that is reported on your W-2. As a result, you don't deduct that amount on your tax return, because it has already been automatically deducted before you even begin your return. But when you send in a contribution on your own to your HSA, that contribution is deductible on your tax return. Your HSA should have a mechanism for making a manual contribution outside of your paycheck.
However, because you started the HSA part way through the year, your contribution limit might be less than the full $3450. In some cases, the contribution limit is prorated based on the number of months you were HSA-eligible. See this answer for an explanation on how the contribution limit works when you are only eligible for part of the year.
Yes. There is no rule about the "spacing" of contributions to an HSA. That is, you don't have to contribute the same amount every month or anything like that. It is perfectly legal to deposit the full amount for the year on January 1. Or to deposit nothing all year and then do it all the last day. For that matter, you are allowed to make contributions against your 2018 limit up to April 15 of 2019, and then take the tax deduction for them on your 2018 taxes. When you make contributions in the beginning of the year, the bank should ask whether these contributions are for the current year or the previous year.