Is it okay to mix in local language when I know it poorly?

Personally I prefer speaking English if my conversational partner isn't reasonably fluent in my other language. "hello", "thank you" & "beer" are always fine as they show some respect for the host culture.

But unless you are fairly fluent and without too much of accent, it's much less work for me if you stay in English.

Usually in countries where knowledge of English is good, and my knowledge of the local language is limited, I generally learn (and use) "hello", "thank you", "goodbye", "do you speak English?" (even if the answer to this is 99 times out of 100, "of course", it feels polite to ask before getting into something more involved in English, like trying to sort out a complicated mistake in a hotel booking), and that's about it, maybe an extremely simple order at a bar e.g. "two beers please".

When I was in Finland a few years ago this seemed to be entirely well-received and caused no problems.

The one time I tried to go beyond this (buying two tram tickets to the city centre), I accidentally asked for one instead of two. My spouse & I both then got on without the driver saying anything more, so I suspect she just silently worked out I wanted two and charged me for the correct tickets, but it's possible she charged me for one, and when she realised I thought I'd bought two decided it wasn't worth saying anything. It didn't actually cause any problems, but it's certainly a situation where it could have done and which would have been avoided if I'd just stuck to doing only basic phatic expressions in Finnish.

Please try the local language whenever you can.

70% of Finns speak English. That number is probably higher in Helsinki and lower in rural areas. It's very likely higher with people working in the tourist industry, but if you travel in rural areas and address older people, you cannot safely assume everybody understands and speaks English. Maybe some speak a bit of Swedish, German, or even Russian, or maybe they are monolingual.

I tried to address a Finnish woman in English once (excuse me, do you speak English?). She shook her head and ran away. This was in a rural area in the far north of Finland (near Kilpisjärvi). I don't know how she would have replied if I had said the equivalent in Finnish (I can't), Swedish (might have worked), or German or Russian (probably not),

I don’t expect it to be considered annoying or anything, but consider the risk of using very limited skills - a mispronounced or mixed up word can easily end with something embarrassing or offensive, and they may or may not realize that it was an accident.

Stick with using the language in situations where you know you can use it, or with people you know better already, and your effort is typically seen as a positive thing.

It depends on what, exactly, you mean in this case.

Introducing yourself in the local language and politely asking to continue the conversation in English (or some other language that you may share with the person in question) is generally OK, and may even result in much more polite treatment by the locals, but at that point you should stick to English baring the particular cases I mention below.

Beyond that, the only times that code-switching seems to be reasonably universally acceptable when talking with strangers and lacking full fluency in both languages involved are meta-linguistic discussions (that is, discussing the language itself), using local place names (which will often also get you more polite responses), or when there is simply no proper translation for the intended concept in the language being spoke (this is part of how loanwords develop).

Code-switching to resolve ambiguity (for example, when the local language distinguishes between concepts that English does not distinguish between) may be considered acceptable, or may not be considered acceptable (when I’ve been traveling and actually done this, it’s seemed to be more acceptable among younger individuals).

Randomly peppering your speech with interjections from the local language though is generally not appreciated, and will usually reinforce that you’re a tourist (which is almost always a bad thing when traveling).