Какая бы погода ни была, моя подруга по-прежнему ходит пешком до метро.

It means whatever the weather is or no matter what the weather is like.

This is a very common Russian pattern:

• какой/какая/какое/какие бы ... ни + past-tense form of быть
• meaning: no matter what ... is/was like

So:

• Какая бы погода ни была = Whatever the weather is

The whole sentence means something like:

• Whatever the weather, my friend still walks to the metro.

Because погода is:

• feminine
• singular
• nominative

So the question word/adjective has to agree with it:

• какая погода = what kind of weather
• not какой погода

Compare:

• какой день = what kind of day
• какая погода = what kind of weather
• какое море = what kind of sea

Because after бы, Russian uses the past-tense form to build a conditional/subjunctive-type structure.

So in this pattern:

• какая бы погода ни была

the word была does not make the meaning past.
It is simply part of the grammar of the construction.

You can think of it as:

• бы + past form = a non-literal, dependent, or hypothetical form

This is why Russian says:

• Что бы ни случилось = Whatever happens
• Куда бы он ни пошёл = Wherever he goes
• Какая бы погода ни была = Whatever the weather is

So the meaning is present/general, even though the form looks past.

Here ни is not ordinary negation. It is part of the fixed concessive pattern:

• что бы ни...
• кто бы ни...
• где бы ни...
• какой бы ни...

This pattern means:

• no matter what
• whoever
• wherever
• however / whatever kind of

So:

• Какая бы погода ни была = No matter what the weather is like

Do not confuse this with не.

• не usually directly negates something
• ни in this structure helps create the meaning no matter...

Because ходит describes a habitual, repeated, regular action.

• ходить = to go on foot regularly / habitually / back and forth
• идти = to be going right now, in one direction, at this moment

In this sentence, the meaning is that she usually or still regularly walks to the metro. So:

• моя подруга по-прежнему ходит пешком до метро

If you said идёт, it would sound like she is walking there right now.

По-прежнему means:

• still
• as before
• just as she used to

So it shows that this has not changed.

In this sentence:

• моя подруга по-прежнему ходит пешком до метро

the idea is:

• she used to walk to the metro before
• and she continues to do so now

It is close to still, but often with a stronger sense of unchanged from before.

Good question. Ходить by itself can mean:

• to go
• to walk
• to travel on foot

But in real Russian, пешком is often added to make it completely explicit that the person goes on foot, not by transport.

So:

• ходит до метро = goes to the metro / travels to the metro
• ходит пешком до метро = goes to the metro on foot

It is very natural to say both together.

Because до means up to / as far as / until reaching that point.

So:

• идти до метро = to walk as far as the metro
• идти к метро = to walk toward the metro

In this sentence, the idea is that the metro is the endpoint of the walking part of the trip. She walks as far as the metro station, then presumably takes the metro.

Also, до requires the genitive case:

• до метро

But метро is indeclinable, so its form does not change.

Because метро is an indeclinable noun in standard Russian.

That means it keeps the same form in different cases:

• метро
• до метро
• к метро
• в метро

Even though до requires the genitive, the word itself stays метро.

Yes. Какая бы погода ни была is a subordinate clause with a concessive meaning:

• whatever the weather is
• no matter what the weather is like

Then comes the main clause:

• моя подруга по-прежнему ходит пешком до метро

So the comma separates:

1. the concessive subordinate clause
2. the main statement

That is why the sentence is written:

• Какая бы погода ни была, моя подруга по-прежнему ходит пешком до метро.

Yes, somewhat. Russian word order is flexible, though some versions sound more natural than others.

The given version is very natural:

• Какая бы погода ни была, моя подруга по-прежнему ходит пешком до метро.

You may also see:

• Моя подруга по-прежнему ходит пешком до метро, какая бы погода ни была.

The meaning stays basically the same.
Putting the concessive clause first makes the contrast clearer right away:

• Whatever the weather, ...

So the original word order is a very good, natural choice.