Are there western governments that don't have to borrow in their own currency? Are there any western and/or democratic countries where the central bank buys all government debt, interest free, directly from the treasury?  I.e. are there any such countries where government spending is effectively financed by money printing without the intermediary of a private market for government bonds?  I don't now for sure, but I suspect this is what happens in autocratic states like China and I wondered if such a regime exists elsewhere.
Edit:  @H2ONaCl is correct that I mean to ask about a case where the central bank holds the interest free debt in perpetuity. Alternatively, and in effect identically, the government just prints money when it wants to spend more than it has.
You have different questions in your title and body I will try to answer them separately:

Are there western governments that don't have to borrow in their own currency?

Yes, all western governments that I know of are allowed to borrow in any currency they want. They usually borrow in their own currency because it is easier for them to repay the debt if they borrow in currency they can control.

Are there any western and/or democratic countries where the central bank buys all government debt, interest free, directly from the treasury?

I do not know of any western government that would get sell this debt interest free  de jure (whether on primary market or not). However, de facto all interest payments that are collected by central banks are send straight back to the government treasury,  so any interest payments that government pays on government bonds are de facto just free and just money juggling - like when government employees have to pay taxes (government first spends money on paying their salaries and then takes some of that money back in taxes instead of paying the post tax salary).

are there any such countries where government spending is effectively financed by money printing without the intermediary of a private market for government bonds?

There are some countries that are not autocratic and do that but are not 'western' countries either. For example, Indonesia is democratic country and their central bank recently started to purchase bonds on primary market.
However, some European central banks are considering it. For example, Bank of England (BOE) recently stated it will:

&quot;keep under review the case for participating in the primary market”, suggesting it could eventually buy bonds from the government or companies directly rather than on secondary markets as it does now.

Nonetheless, this has nothing to do with the interest payments themselves, they will likely not be eliminated (and why would it even matter given that the government essentially pays that interest to itself?).
Fed now has a program to buy bonds on primary market from companies, but not from government.
Czech republic recently tried to fast-track a bill that would allow their central bank to do that, but only during financial crises, but the motion failed. However, it is possible the bill will pass in the future (this was only fast-track process that would skip debate with experts/scientists and public debate).