W mojej torbie zawsze jest mała apteczka, więc mam tam też chusteczki i termometr.

Because the preposition w meaning in takes the locative case when it describes location.

So:

• moja torba = my bag (dictionary/basic form)
• w mojej torbie = in my bag

Both words change because they must match in case, gender, and number:

• moja → mojej
• torba → torbie

This is a very common Polish pattern:

• w domu = in the house
• w szkole = at school
• w mojej torbie = in my bag

Because in the first clause, the thing that is in the bag is mała apteczka — a small first-aid kit — and that noun is singular.

So:

• mała apteczka = singular
• therefore jest = singular is

Even though the sentence later mentions chusteczki i termometr, those belong to the second clause:

• mam tam też chusteczki i termometr = I also have tissues and a thermometer there

The two clauses work separately:

1. W mojej torbie zawsze jest mała apteczka
2. więc mam tam też chusteczki i termometr

Because here apteczka is the thing that exists or is located somewhere, so it stays in the nominative case.

Pattern:

• W torbie jest apteczka = There is a first-aid kit in the bag

Polish often uses nominative after być in sentences of existence/location.

Compare that with a different use of być:

• Ona jest lekarzem = She is a doctor

Here lekarzem is instrumental because it identifies what someone is.

So in your sentence:

• mała apteczka is not a role or profession
• it is simply the thing that is in the bag
• so nominative is correct

Yes, it is related to apteka (pharmacy), but apteczka does not mean little pharmacy in normal English.

In real usage, apteczka means:

• first-aid kit
• medical kit
• sometimes medicine kit

So mała apteczka is most naturally understood as a small first-aid kit.

It is best to learn apteczka as its own everyday word, not by translating it literally piece by piece.

Because mam expresses possession: I have.

• mam chusteczki i termometr = I have tissues and a thermometer

Polish often uses mieć just like English to have.

You could also say:

• ... więc są tam też chusteczki i termometr

That would mean:

• ... so there are also tissues and a thermometer there

Both are possible, but the nuance is a little different:

• mam focuses on what I have in my bag
• są focuses on what is located in the bag

The original sentence sounds natural because the speaker is talking about what they keep with them.

więc means so, therefore, or thus. It introduces a result.

• mam apteczkę, więc mam też termometr
  = I have a first-aid kit, so I also have a thermometer

By contrast, bo means because and introduces a reason.

Compare:

• Mam termometr, bo mam apteczkę = I have a thermometer because I have a first-aid kit
• Mam apteczkę, więc mam termometr = I have a first-aid kit, so I have a thermometer

So:

• bo = because
• więc = so / therefore

Because in Polish, więc is normally preceded by a comma when it connects clauses.

So this is standard:

• W mojej torbie zawsze jest mała apteczka, więc mam tam też chusteczki i termometr.

This is similar to English punctuation before so when two full clauses are joined.

• tam = there
• też = also / too

So:

• mam tam też chusteczki i termometr = I also have tissues and a thermometer there

In this sentence, tam refers back to w mojej torbie — basically in there / in my bag.

And też adds the idea of also:

• not only the first-aid kit
• but also tissues and a thermometer

No, it is not strictly necessary.

You could say:

• W mojej torbie zawsze jest mała apteczka, więc mam też chusteczki i termometr.

That still makes sense.

Adding tam does this:

• it makes the location a little more explicit
• it sounds like I have them there too / in there too

So tam is natural, but optional.

chusteczki is the plural of chusteczka.

It can mean:

• tissues
• wet wipes
• sometimes small napkins, depending on context

In everyday speech, the plural is very common because people usually carry or use more than one tissue:

• Mam chusteczki = I have tissues
• Daj mi chusteczkę = Give me a tissue

So the plural here is completely natural.

Because termometr is a masculine inanimate noun, and in Polish, the accusative singular of masculine inanimate nouns is usually the same as the nominative singular.

So:

• nominative: termometr
• accusative: termometr

That is why:

• mam termometr = I have a thermometer

Compare that with a masculine animate noun:

• widzę psa = I see a dog
• nominative: pies
• accusative: psa

So termometr does not visibly change because of its gender/type.

Yes. Polish word order is more flexible than English, although different orders change the emphasis.

Original:

• W mojej torbie zawsze jest mała apteczka, więc mam tam też chusteczki i termometr.

Possible variations:

• Zawsze w mojej torbie jest mała apteczka...
• Mała apteczka zawsze jest w mojej torbie...
• ... więc też mam tam chusteczki i termometr.

These versions are grammatically possible, but the original sounds natural and balanced.

Very roughly:

• putting something earlier often emphasizes it
• putting something later often makes it the new or important information

For learners, the original version is a good model to copy.

It changes because mojej has to match the noun torbie in case, gender, and number.

mój / moja / moje behaves like an adjective, so it changes form just like adjectives do.

Here:

• torba is feminine singular
• after w for location, it becomes torbie in the locative
• so moja must also become locative feminine singular: mojej

That is why you get:

• moja torba = my bag
• w mojej torbie = in my bag

So yes, it is possessive in meaning, but grammatically it follows adjective-style endings.

zawsze means always, and here it modifies the whole idea that the first-aid kit is in the bag.

So:

• W mojej torbie zawsze jest mała apteczka = There is always a small first-aid kit in my bag

It tells you this is not occasional:

• not sometimes
• not right now only
• but as a regular habit

Its position is natural, but Polish allows some flexibility:

• Zawsze w mojej torbie jest mała apteczka
• W mojej torbie jest zawsze mała apteczka

The original version is the most neutral and common-sounding.