Bei diesem Verb ändert sich der Stamm in der Vergangenheit, und die Wortart bleibt trotzdem dieselbe.

Because bei always takes the dative case.

• das Verb is a neuter noun
• dative singular of dieses is diesem

So:

• nominative: dieses Verb
• dative: bei diesem Verb

In this sentence, bei diesem Verb means something like with this verb or in the case of this verb.

Here, bei does not mean physical location like next to. It has a more abstract meaning: in the case of, with, or when dealing with.

So Bei diesem Verb means:

• With this verb
• In this verb
• When it comes to this verb

That is a very common use of bei in German.

Here, yes: sich ändern means to change in the sense of to become different.

So:

• etwas ändern = to change something
  
  • Ich ändere den Plan. = I change the plan.
• sich ändern = to change / to undergo change
  
  • Der Plan ändert sich. = The plan changes.

In your sentence, der Stamm is the thing that changes, so German uses the reflexive form:

• der Stamm ändert sich = the stem changes

In grammar, der Stamm means the stem of a word, especially the basic part before endings are added.

With verbs, it is the core form that endings attach to. For example:

• machen → stem: mach-
• lernen → stem: lern-

In this sentence, it refers to the fact that some verbs change their stem in past forms, for example:

• singen → sang
• gehen → ging

So der Stamm here means the verb stem.

In der Vergangenheit means in the past.

It uses der because Vergangenheit is a feminine noun:

• die Vergangenheit

Here, in is followed by the dative because it is used in a non-directional, abstract sense.

So:

• nominative: die Vergangenheit
• dative: in der Vergangenheit

This phrase is a standard way to say in the past.

German main clauses normally follow the verb-second rule.

That means the finite verb must come in the second position. The first position can be taken by different elements, not just the subject.

Here the first position is:

• Bei diesem Verb

So the finite verb comes next:

• ändert

Then the rest follows:

• sich der Stamm

So the structure is:

• Bei diesem Verb / ändert / sich der Stamm

If you started with the subject instead, you could also say:

• Der Stamm ändert sich bei diesem Verb.

That is also grammatical, but it has a slightly different emphasis.

Because after und, German usually starts a new main clause, and main clauses also follow the verb-second rule.

So in the second clause:

• first position: die Wortart
• second position: bleibt

Then the other elements follow:

• trotzdem dieselbe

So:

• und die Wortart bleibt trotzdem dieselbe

is a normal main-clause word order.

Wortart means part of speech or word class.

Examples of Wortarten are:

• noun
• verb
• adjective
• adverb
• pronoun

So the sentence is saying that even though the verb stem changes in the past, the word still belongs to the same grammatical category: it is still a verb.

Dieselbe means the same one.

It matches Wortart, which is:

• feminine
• singular

So the form is:

• die Wortart
• dieselbe

German uses this form because the sentence is saying the word class remains the same.

You can think of it as:

• die Wortart bleibt dieselbe = the word class stays the same

Trotzdem means nevertheless, all the same, or despite that.

It shows contrast:

• the stem changes in the past
• but the word class still does not change

So trotzdem highlights the idea:

• even so
• despite this change

In English, the full sense is something like:

• the stem changes in the past, but the part of speech still remains the same

Most likely, yes. It sounds like a grammar explanation about verbs whose stem changes in past forms.

Typical examples are:

• singen → sang
• finden → fand
• gehen → ging

The point of the sentence is that even if the stem changes, the word does not become a different kind of word. It is still a verb.