Стоит мне лечь спать, как телефон начинает звенеть.

Here стоит is part of the fixed pattern стоит кому-то что-то сделать, как...

In this pattern, it means something like:

• it only takes someone to do X for Y to happen
• as soon as someone does X, Y happens
• no sooner does someone do X than Y happens

So:

Стоит мне лечь спать, как телефон начинает звенеть.
= As soon as I lie down to go to sleep, the phone starts ringing.

This is an idiomatic construction, so you should learn it as a whole rather than trying to translate стоит word by word.

Because this construction uses the dative case for the person involved:

• стоит мне...
• стоит тебе...
• стоит ему...

So the pattern is:

стоит + dative + infinitive, как...

Examples:

• Стоит тебе выйти, как начинается дождь.
  As soon as you go out, it starts raining.

• Стоит ему позвонить, как все меняется.
  As soon as he calls, everything changes.

So мне is not the subject in the usual nominative sense; it is required by this idiom.

Because лечь is perfective, and ложиться is imperfective.

• лечь = to lie down, to go to bed as a single completed action
• ложиться = to be lying down / to lie down habitually / to be in the process of going to bed

In this sentence, the meaning is:

the moment I lie down / go to bed

That calls for the perfective infinitive лечь, because it refers to the action as a completed trigger.

So:

• Стоит мне лечь... = As soon as I lie down...
• Стоит мне ложиться... would sound wrong or at least unnatural here

Yes, лечь by itself means to lie down, but лечь спать is a very common expression meaning:

• to go to bed
• to lie down to sleep

Without спать, the sentence could simply mean physically lying down somewhere, not necessarily going to sleep.

Compare:

• лечь на диван = to lie down on the sofa
• лечь в кровать = to lie down in bed
• лечь спать = to go to bed / lie down to sleep

So спать makes the intended meaning clear.

Correct: here как does not mean how.

In this construction, как introduces the second event that happens immediately after the first one:

Стоит мне лечь спать, как телефон начинает звенеть.

This is a set correlative pattern:

Стоит..., как...

It means:

• as soon as...
• no sooner... than...

So you should not interpret как separately as how here. It is part of the whole structure.

Начинает звенеть means starts ringing. It emphasizes the beginning of the ringing right after the speaker goes to bed.

So the sentence gives a vivid sequence:

1. I lie down to sleep.
2. The phone immediately starts ringing.

If you said телефон звонит, that would mean the phone is ringing / the phone rings, which is possible in some contexts, but начинает звенеть highlights the sudden start of the action.

Also, звенеть literally means to ring or to jingle, and with a phone it refers to the ringing sound.

Because the two verbs are doing different jobs.

1. лечь is perfective

It marks the first action as a single completed event that triggers the next one:

• Стоит мне лечь...
  As soon as I lie down...

2. начинает is imperfective

начинает is the present tense of начинать (to begin / to start), which is imperfective. Here it describes what typically happens in this repeated situation:

• every time I go to bed, the phone starts ringing

So the whole sentence expresses a habitual pattern, not one single event happening right now.

Normally, it describes a repeated pattern or an annoying habit of events:

• Every time I go to bed, the phone starts ringing.
• As soon as I lie down to sleep, the phone starts ringing.

Russian often uses the present tense for this kind of general repeated situation.

If you wanted to describe one specific past occasion, you would usually change the tense:

• Стоило мне лечь спать, как телефон зазвонил.
  As soon as I lay down to sleep, the phone rang.

Yes, normally yes.

In this construction, the first clause and the second clause are separated by a comma:

Стоит мне лечь спать, как телефон начинает звенеть.

That is the standard punctuation because как introduces the following clause.

No — and this is a very important distinction.

1. Стоит мне лечь спать, как...

This is the idiom we are discussing:

• As soon as I go to bed, ...
• No sooner do I go to bed than...

2. Мне стоит лечь спать

This is a different structure meaning:

• I should go to bed
• It would be a good idea for me to go to bed

So word order matters a lot here.

Compare:

• Стоит мне лечь спать, как телефон начинает звенеть.
  As soon as I go to bed, the phone starts ringing.

• Мне стоит лечь спать.
  I should go to bed.

These are completely different meanings.

The most natural translations are:

• As soon as I lie down to sleep, the phone starts ringing.
• Every time I go to bed, the phone starts ringing.
• No sooner do I go to bed than the phone starts ringing.

The last one is closer to the Russian structure, but in everyday English the first two often sound more natural.

Yes, absolutely. This is a useful and fairly common literary/neutral pattern, and it is best learned as a whole:

Стоит кому-то что-то сделать, как...

Meaning:

• as soon as someone does something, something else happens

More examples:

• Стоит ему заснуть, как соседи начинают шуметь.
  As soon as he falls asleep, the neighbors start making noise.

• Стоит нам выйти из дома, как начинается дождь.
  As soon as we leave the house, it starts raining.

• Стоит ей улыбнуться, как все сразу добреют.
  As soon as she smiles, everyone immediately softens.

So yes: treat it as a ready-made structure.