אם הדפדפן נתקע, תסגרי אותו ותפתחי אותו עוד פעם.

Yes. Formally, תסגרי and תפתחי are 2nd-person feminine singular future forms.

In everyday modern Hebrew, though, these future forms are very often used as commands, especially in speech. So instead of the textbook imperative סגרי and פתחי, many speakers naturally say תסגרי and תפתחי.

So this sentence is colloquial and very natural.

A more textbook-style version would be:

אם הדפדפן נתקע, סגרי אותו ופתחי אותו שוב.

Because תסגרי and תפתחי are specifically 2nd-person feminine singular.

Hebrew verbs change depending on who is being addressed.

Other versions would be:

• to one man: אם הדפדפן נתקע, תסגור אותו ותפתח אותו עוד פעם
• to several people: אם הדפדפן נתקע, תסגרו אותו ותפתחו אותו עוד פעם

So the original sentence is directed at one female listener.

This is a very good question, because נתקע can look ambiguous.

In this pattern, the masculine singular past form and the masculine singular present form can be identical in writing. So נתקע can be understood from context.

Here, because it appears after אם and is followed by instructions, it means something like:

• gets stuck
• freezes
• is stuck

So in this sentence, it is understood as a present/future-type condition, not as a finished past event.

Because it agrees with הדפדפן.

The noun דפדפן is masculine singular, so the verb is also masculine singular:

• הדפדפן נתקע

If the subject were a feminine singular noun, the form would change. For example, with התוכנה you would expect:

• אם התוכנה נתקעה...

Hebrew agreement is very important: verbs often reflect the gender and number of the subject.

אותו is the direct-object pronoun meaning him or it, depending on context.

Here it refers back to הדפדפן, so it means it.

A useful way to think of it is:

• תסגרי אותו = close it
• תפתחי אותו = open it

Because דפדפן is masculine singular, the pronoun is אותו.
If the noun were feminine singular, you would use אותה.

Also, do not confuse אותו with איתו:

• אותו = him / it as a direct object
• איתו = with him / with it

Because each verb has its own direct object.

The structure is:

• תסגרי אותו
• ותפתחי אותו

Hebrew normally expresses the object with each verb in a sequence like this. That makes the sentence clear and natural.

In English, you also usually repeat the object in a similar sentence:

• close it and open it again

So the Hebrew repetition is not unusual.

עוד פעם literally means one more time, but in everyday Hebrew it very often means again.

So here it means again.

Yes, you can also say שוב. In many cases, both work:

• ותפתחי אותו עוד פעם
• ותפתחי אותו שוב

A rough difference is:

• עוד פעם sounds more conversational and spoken
• שוב can sound a bit shorter, neater, and sometimes slightly more neutral or written

Both are perfectly normal.

The prefix ה־ is the definite article, so הדפדפן means the browser.

Hebrew often uses the definite form when referring to the relevant thing in the situation, even when English might be a little looser. In a context like computer instructions, the browser simply means the browser you are dealing with.

So הדפדפן sounds completely natural here.

Yes. This sentence is quite conversational. A more formal or more standard-looking version could use:

• the imperative instead of the future-form command
• שוב instead of עוד פעם

For example:

אם הדפדפן נתקע, סגרי אותו ופתחי אותו שוב.

You may also see a version with a more explicit future in the אם clause:

אם הדפדפן ייתקע, סגרי אותו ופתחי אותו שוב.

All of these are understandable, but the original sentence sounds very natural in everyday spoken Hebrew.