Domestic made

我很少看到这个词语
感觉是 外国人能少注重于 国产或者外企的品牌，都是看质量吧

Take this Oppo mobile phone I use now for example, domestic cell phones have made great progress in their quality than they were three years ago.

For example 就好了
第一句 很明显的中文思维。 我还是翻译成中文才看懂。
make great progress 很奇怪
后面的部分最好改成两个部分。
大概就是 ( 最好详细的指出是哪个牌子）

They are not worse than any global mobile brands and could be better than those.

not worse 不行
on a par with 这个词组可以学学
The quality of Xiaomi's products is on par with Apple.

If you need a new mobile phone right now, please choose a domestic one.

rewrite this one.

I promise, trust me.

口语化
不正式
没有人这样说的
最好删了

Take this Oppo mobile phone I use now foras an example, domestic cell phones have made great progress in their quality than they werecompared to three years ago.

They are not worse than any other global mobile brands, and could even be better than thosem.

Take this Oppo mobile phone I use now, for example,. It shows that domestic cell phones have made great progress in theiare much better quality than they were three years ago.

You need a period because the first sentence doesn't link up with the second in any way (grammatically). You haven't said what the Oppo is an example of. And 'than' requires a explicit comparison. You can say either 'cell phones have made great progress in quality in the last 3 years' OR 'cell phones are much better quality now than they were 3 years ago'.

They are not worse than anyat least as good as any of the global mobile brands and could bsome are better than those.

'Any' is singular and 'brands' is plural, so you need to add a couple of words to make sense. 'Not worse' is a negative way of making the comparison; at least as good is much more positive.

I promise, you won't be sorry. You can trust me.

(1) What are you promising? (2) You need a period or some way of linking the two sentences grammatically, and I can't think of a good way to do the latter. (Yes, many native speakers make this error, creating 'run-on sentences', but that's no reason to learn the error.)