I think you understand the distinction between 'hope to' and 'hope that...'.
Your use of the verb 'to hope' is correct.
Hope to... is always followed by a verb (infinitive), e.g. I hope to see you again next month.
Hope that... is simply the introduction to a 'new' sentence that is announced by 'that', so it is followed by a new sentence, e.g. I hope that I will see you again next month.
This being said, there are some other small typing- and other errors in your text (you might want to use a spellchecker) that I've highlighted in colors.
1. We hope that our service will give the most satisfaction to all our clients who are dealing with us. (Redundant: you can delete this, because you don't have clients who do not deal with you). I would also consider removing 'the most' as it is a bit 'over the top'.
We hope that our service will be as satisfactory to you as it has been to all our customers.
2. We can promise that we meet it within a week if you decide to palce an order
Don't say what you can promise, just promise it, or commit to it. We promise that...
the use of that is not wrong here, but why not be a bit more direct, and write We promise to meet...
You should define 'it' more clearly. I'm assuming that you're referring to either a deadline or a customer's wish? You can write it explicitly.
This is not wrong, but it could be more direct, shorter: when you...
palce --> place
Or change it to something like this:
We promise to deliver within a week upon reception of your order.
3. We hope you find our products satisfactory.
If you're really convinced about your quality, you might want to replace 'hope' by 'trust'. We trust it... We are sure that...
4. I will vist your company (or I will visit you which one sounds better?)
vist --> visit
Both are correct, but I will visit you is more personal (I would prefer it for that reason).
I hope this helps!
- For Teachers