kono bunpou no rensyuumondai wo hitori de yatte mimasu.

Here, の links two nouns.

So 文法の練習問題 means something like:

• grammar practice problems
• practice problems for grammar
• practice questions on this grammar point

It does not have to mean possession. In Japanese, A の B can mean many relationships, including B related to A, B for A, or B about A.

Grammatically, この directly modifies 文法, because この must come right before the noun it describes.

So the structure is:

• この文法 = this grammar / this grammar point
• この文法の練習問題 = practice problems for this grammar point

In natural English, you might translate the whole phrase more smoothly as these grammar practice problems, but the Japanese structure is literally closer to the practice problems for this grammar.

を marks the direct object of the verb.

The thing being done is:

この文法の練習問題

So the sentence is saying that the speaker will do or try doing those practice problems.

一人で means by oneself, alone, or on one’s own.

In this sentence, で marks the manner or condition in which the action is done. So 一人で tells you how the speaker will do the practice problems: without another person’s help or company.

Examples:

• 一人で行きます。 = I’ll go by myself.
• 一人で食べます。 = I eat alone.
• 一人でやってみます。 = I’ll try doing it on my own.

Here it is read ひとり.

So:

• 一人で = ひとりで

This is one of the irregular person-counter readings:

• 一人 = ひとり
• 二人 = ふたり

After that, they become more regular:

• 三人 = さんにん
• 四人 = よにん

やってみます is:

• やる in the て-form → やって
• plus みます from みる

The pattern 〜てみる means to try doing something.

So やってみます means:

• I’ll try doing it
• I’m going to give it a try

Important point: in this grammar pattern, みる does not mean literal seeing with the eyes. It functions as a helper verb meaning try and see what happens.

Both can be used for doing exercises or tasks.

• 練習問題をする = a very standard, neutral way to say do practice problems
• 練習問題をやる = also very common, and often a bit more conversational

So やってみます sounds natural here.

A version with する is also possible:

• この文法の練習問題を一人でしてみます。

That is grammatical too, but やる is very common for exercises, homework, and tasks.

Japanese ます-form is non-past, so it can refer to either present or future depending on context.

Here, it is most naturally understood as future/intention:

• I’ll try doing these practice problems by myself.
• I’m going to try doing these by myself.

So even though Japanese does not have a separate future tense form here, the meaning is future-looking.

Yes. Japanese word order is more flexible than English, as long as the particles stay attached to the right words.

For example, these are both natural:

• この文法の練習問題を一人でやってみます。
• 一人でこの文法の練習問題をやってみます。

The basic meaning stays the same. Moving 一人で earlier can put slightly more attention on by myself.

They are probably included just to help learners read the sentence more easily.

In normal Japanese writing, you would usually write it without spaces:

この文法の練習問題を一人でやってみます。

Japanese normally does not separate words with spaces the way English does.