No, the second one is wrong.

We say:

Une bouteille de bière (A bottle of beer).

We only use the de to say “a bottle of beer”.

Therefore, we also say:

J’ai bu de la bière (I drank (some) beer).

The first sentence is correct.
You cannot say “Je donne de bière à Jean” as there is no quantity noun.

Quantities, Weights, Measures in French must be followed by de + noun without the definite or partitive article. For example, a kilogram of oranges = un kilo d’oranges, NOT un kilo des pommes.

No, de la (as well as du, des and de l’) is the partitive article. It is required when talking about things which – as a general but not absolute rule – can be counted. English does not require this. ‘I have money’. ‘I am eating fruit’. And so on. In French, that would be j’ai de l’argent and je mange du fruit.

The rules are:

• masculine singular – du

• feminine singular – de la

• masculine or singular beginning with vowel – de l’

• plural – des

So in your example, it would be, je donne de la bière.

However, if you’re sitting there with a bottle in your hand and hand it to someone, it would be je donne la bière, but only because you’re talking about one particular beer.