Termometre bozulursa yenisini almadan olmaz.

Bozulursa means if it breaks / if it goes bad / if it stops working.

It breaks down like this:

• bozul- = to break, get spoiled, go wrong, stop working
• -ur = aorist marker, often used in general statements or future-like conditions
• -sa = if

So bozulursa literally means if it breaks or if it happens to break.

Not exactly, even though it looks similar to a passive form.

• bozmak = to break/spoil something
  • Termometreyi bozdu. = He/she broke the thermometer.
• bozulmak = to break, go bad, stop working
  • Termometre bozuldu. = The thermometer broke / stopped working.

So in this sentence, termometre bozulursa means if the thermometer breaks, not necessarily if it is broken by someone.

Because yeni by itself is usually just an adjective: new.

Here Turkish needs something like the new one or a new one, because the noun termometre is omitted but understood from context. That is why Turkish uses:

• yenisi = the new one / its new one
• yenisini = the new one as the object of the verb

So yenisini almak means to buy/get a new one.

They each have a job:

• yeni = new
• yenisi = the new one
  The -si helps turn the adjective into a noun-like form when the actual noun is omitted.
• yenisini = the new one as a direct object
  The -ni is the accusative ending.

So:

• yenisi = the new one
• yenisini almak = to buy/get the new one, or more naturally in English, to buy a new one

Almadan means without buying / without getting / without taking.

It comes from:

• almak = to take, get, buy
• -madan / -meden = without doing

So:

• almadan = without buying/getting

This ending is very common in Turkish:

• yemeden = without eating
• gitmeden = without going
• sormadan = without asking

That is normal. Almak is a broad verb and can mean take, get, receive, or buy, depending on context.

In this sentence, since we are talking about replacing a broken thermometer, the natural meaning is buy or get:

• yenisini almak = to buy/get a new one

Turkish often uses almak where English specifically uses buy.

This is an important Turkish pattern.

• X-madan olmaz literally means something like it won’t do without X-ing
• More naturally in English: you can’t do without X-ing or it is necessary to X

So:

• yenisini almadan olmaz = you have to buy a new one
• literally: it won’t be possible without buying a new one

It is an impersonal, idiomatic way to express necessity.

Because Turkish often leaves the subject out when it is obvious, general, or not important.

In yenisini almadan olmaz, the idea is generic:

• one can’t do without buying a new one
• you have to buy a new one
• we’ll need to buy a new one

English usually chooses a subject, but Turkish often does not need one.

They are similar, but not the same.

• bozulursa = if it breaks / if it should break
  This sounds general, future, or hypothetical.
• bozulduysa = if it has broken / if it turns out it broke
  This refers more to a past or already-completed situation.

So the original sentence sounds like a general rule:

• If the thermometer breaks, we’ll have to buy a new one.

If you said Termometre bozulduysa..., it would sound more like:

• If the thermometer has broken...

Yes. Turkish has several natural ways to express the same basic idea. For example:

• Termometre bozulursa yenisini almak gerekir.
  = If the thermometer breaks, it is necessary to buy a new one.
• Termometre bozulursa yeni bir tane almak lazım.
  = If the thermometer breaks, it’s necessary to buy a new one.

The original yenisini almadan olmaz is a little more idiomatic and has the sense of there’s no way around buying a new one.