Im Browser habe ich nur einen Tab offen, wobei ich die anderen Tabs später wieder öffnen kann.

Im is just the contraction of in dem.

• in dem Browser = in the browser
• im Browser = same meaning, but more natural in everyday German

German very often contracts:

• in dem → im
• an dem → am
• zu dem → zum
• zu der → zur

So Im Browser is the normal phrasing here.

German often uses haben + object + adjective to express that someone is keeping something in a certain state.

So:

• Ich habe einen Tab offen. = I have a tab open.
• literally: I have one tab in an open state.

This is different from:

• Ein Tab ist offen. = A tab is open.

The first version focuses on what I have open.
The second focuses on the tab itself being open.

Because einen Tab is the accusative form of ein Tab.

The noun Tab is masculine in German: der Tab.

So the forms are:

• nominative: ein Tab
• accusative: einen Tab

In this sentence, einen Tab is the direct object of habe, so it must be in the accusative:

• Ich habe einen Tab offen.

Offen is an adjective meaning open.
Öffnen is a verb meaning to open.

So:

• Ich habe einen Tab offen. = I have one tab open.
• Ich öffne einen Tab. = I open a tab.

In your sentence:

• offen describes the state of the tab now
• öffnen later in the sentence describes the action of opening the other tabs again

This is a very common pattern in German:

• Ich habe die Tür offen.
• Ich habe das Fenster auf.

Because it belongs to the structure haben + object + adjective.

The core pattern is:

• ich habe
  • einen Tab
    • offen

Here, offen is not the main verb. The finite verb is habe, which stays in second position in a main clause.
Offen comes later as a complement describing the object.

Compare:

• Ich habe die Tür offen.
• Sie hat das Fenster zu.
• Wir haben den Computer an.

So the position of offen is normal.

Wobei can be tricky because it has several uses. Here it means something like:

• while
• though
• with the proviso that
• and at the same time

In this sentence, it adds an extra piece of information:

• Im Browser habe ich nur einen Tab offen, wobei ich die anderen Tabs später wieder öffnen kann.

A natural English sense is:

• I only have one tab open in the browser, though I can reopen the other tabs later.
• I only have one tab open in the browser, and I can reopen the other tabs later.

So wobei here connects the first statement with a related clarifying point.

Because wobei introduces a subordinate clause.

In German subordinate clauses, the conjugated verb usually goes to the end:

• ..., wobei ich die anderen Tabs später wieder öffnen kann.

The verb phrase is öffnen kann, and the finite verb kann comes at the end.

Compare:

• Ich bleibe zu Hause, weil ich müde bin.
• Sie lernt Deutsch, obwohl es schwer ist.
• Er spart Geld, wobei er später reisen kann.

So the word order after wobei is normal subordinate-clause word order.

Because in a subordinate clause, the verb cluster goes to the end.

Main clause:

• Ich kann die anderen Tabs später wieder öffnen.

Subordinate clause:

• ..., wobei ich die anderen Tabs später wieder öffnen kann.

So kann moves to the end because of wobei.

Also, wieder öffnen means open again / reopen.

Here wieder means again.

So:

• die anderen Tabs später wieder öffnen = open the other tabs again later / reopen the other tabs later

In context, the idea is that those tabs were open before, or can be brought back later.

German wieder can sometimes mean:

• again
• back

Here both ideas are close, and in English reopen is often the most natural translation.

Yes, both are possible.

• Im Browser habe ich nur einen Tab offen.
• Ich habe im Browser nur einen Tab offen.

German allows a lot of flexibility by putting different elements in the first position. The first position is often used for topic or emphasis.

Starting with Im Browser puts the focus on the setting:

• As for the browser, I only have one tab open.

Starting with Ich is more neutral:

• I only have one tab open in the browser.

So the original sentence is not unusual; it just foregrounds the browser.

Die anderen Tabs means the other tabs — specific tabs that are already understood from the context.

Since the sentence already mentions one tab, the phrase the other tabs naturally refers to the remaining ones.

Compare:

• die anderen Tabs = the other tabs, the remaining tabs
• andere Tabs = other tabs in a more general sense

So here die anderen Tabs is the natural choice because these are specific tabs the speaker already has in mind.

Nur means only.

In this sentence:

• habe ich nur einen Tab offen

it limits the number of open tabs to one.

So the meaning is:

• I have only one tab open.

If you moved nur, the emphasis could change slightly, although the basic meaning might remain similar. In the given sentence, nur clearly modifies einen Tab.

Yes, it is natural German.

A few points make it sound idiomatic:

• im Browser is a normal contraction
• einen Tab offen haben is a very common German structure
• die anderen Tabs später wieder öffnen is perfectly natural
• wobei is a slightly more sophisticated connector, but still standard and natural

A slightly simpler alternative would be:

• Im Browser habe ich nur einen Tab offen, aber ich kann die anderen Tabs später wieder öffnen.

That version uses aber, which may be easier for learners. But the original sentence is fully correct and natural.