Just to add to the good advice you've already been given.
First, there is absolutely no question of you needing to obtain permission from the company before you can review their products. And, if you do write a review, you most definitely should not submit it to the company before publication. If that was not the case, nobody would ever be able to write a negative review, and the whole concept of reviews would be worthless.
Regarding copyright: if you use a photo or other material from the company's website, and use it in your review without their permission, you risk infringing their copyright. I use the word "risk" because in most countries there is a defence of "fair usage" or "fair dealing". This explicitly says that you can use small extracts from a work specifically for the purpose of a review (amongst other things).
Of course, any photos you take yourself for the purpose of your review will be your copyright, so the issue wouldn't arise.
Now, although you've got a perfect legal right to review this particular company's products, if I were you, I would think twice about doing so. They sound like the sort of people who are out to make trouble, and could well try some heavy-handed legal stuff on you, however unjustified. And besides, why should you do them the favour?
Finally, I suggest that if you come across any new company's products that you want to review, don't even ask their permission. Just go ahead and do it.