All of those examples sound somewhat strange to me, and several of them contain other grammatical errors that suggest they were not composed by a native speaker. The recommend you to... construction is marginal compared to recommend that you..., as you can see from this Google Ngrams chart.
I've rewritten below the sentences as I would prefer them, with my changes highlighted.
We recommend that you update your browser
We recommend that you use REGULAR ELICINA, which does not contain any moisturizers, which is good for it will avoid the greasiness of the skin
It's more natural in this sentence to use a relative clause beginning with which than with that, since the clause seems to contribute additional information rather than specify a particular entity, like in the noun phrase the man that I saw, where that I saw helps you pick out exactly which man I'm talking about.
3) We recommend that you check the privacy policies of such service providers to understand how they process your location data
4) If your plans are to apply for a permanent visa, Escalar recommends that you contact Arrive Australia Migration Services for additional information
You can contact someone, but it sounds decidedly strange to contact with someone, so I've deleted that preposition from the original sentence.
5) To avoid the Megaproject Paradox, we recommend that you study the points described above, and report to your management and sponsors
It looks like this sentence is incomplete so I'm not sure what it's supposed to be, but it seems like it should be report to your management and sponsors and not report your management and sponsors. The noun sponsors should not be capitalized.
Note that these judgments are strictly for American English and I cannot comment on how these sentences fare in other varieties of English.