Если я не могу найти ключ, я начинаю искать его в сумке.

They are a very common aspect pair, but they do not mean exactly the same thing.

• найти = to find, with focus on the result
• искать = to look for / search for, with focus on the process

So:

• не могу найти ключ = I cannot find the key
• начинаю искать его = I start looking for it

In other words, first the speaker says the result is not happening, and then says they begin the process of searching.

After начинать / начать, Russian normally uses an imperfective infinitive, because you begin an activity or process.

So:

• начинаю искать = I begin searching

That sounds natural, because searching is an ongoing action.
But начинаю найти would sound wrong, because найти is perfective and refers to a completed result, not an activity you can really start doing step by step.

Ключ is the direct object of найти, so it is in the accusative case.

However, for inanimate masculine singular nouns, the accusative looks the same as the nominative.

So:

• nominative: ключ
• accusative: ключ

That is why there is no visible ending change here.

Because его is the correct object pronoun, while он is the subject pronoun.

• он = he / it, used as the subject
• его = him / it, used as the object

Here, the pronoun refers back to ключ and is the object of искать, so Russian uses его.

After в, Russian can use different cases depending on the meaning:

• в + prepositional = location, in
• в + accusative = motion, into

Here the meaning is location, so:

• в сумке = in the bag

If you said в сумку, that would mean movement into the bag, not location inside it.

Russian often leaves out possessives such as my, your, or his/her when the owner is obvious from context.

So в сумке can naturally mean:

• in the bag
• in a bag
• in my bag

If the speaker wants to make it explicit, they can say:

• в моей сумке = in my bag

But in everyday Russian, leaving it out is very common.

Russian has no articles, so there is no direct equivalent of a or the.

Whether a noun is understood as definite or indefinite comes from context.

In this sentence, ключ will usually be understood as the key, because the speaker probably means a specific key they are trying to locate. But Russian itself does not mark that with a separate word.

Because Если я не могу найти ключ is a subordinate clause introduced by если.

Russian normally separates a subordinate clause from the main clause with a comma:

• Если ... , ...

So the comma is standard grammar here.

Yes, it can sometimes be omitted, but repeating it is very normal.

• Если я не могу найти ключ, я начинаю искать его в сумке.
• Если я не могу найти ключ, начинаю искать его в сумке.

Both are possible.

Repeating я makes the structure clearer and sounds neutral. Leaving it out is also possible when the subject is easy to understand from context.

Its basic meaning is if, but in habitual situations English may naturally translate it as when or whenever.

So this sentence can describe:

• a real condition: If I can’t find the key, ...
• a repeated pattern: When / Whenever I can’t find the key, ...

Russian still uses если in that kind of repeated-condition statement.

Yes. Russian word order is more flexible than English because case endings show grammatical roles.

The version here is neutral:

• я начинаю искать его в сумке

But other orders are possible, for example:

• я начинаю его искать в сумке
• в сумке я начинаю искать его

These alternatives change emphasis more than basic meaning. The original order is a straightforward, natural one for learners to use.