Only the bless effect

Dispel magic specifies that it ends...

Any spell ... on the target

While the bless effect is simply a spell effect, it still qualifies as a spell for this purpose as evident by this ruling by Jeremy Crawford, lead designer for 5e:

Dispel magic can be used against a spell effect created by a potion

Some tangential evidence: this answer to another question also addresses that dispel magic can work against spell effects without having to dispel an entire actual spell.

Dispel magic ends a spell on one target. It doesn’t end the same spell on other targets.

So you would dispel any magical effect that is a spell effect, but not the additional effect such as the temporary hit points of the potion of heroism.

Fake brews: They won't get you drunk

Liquids generally aren't considered valid objects, so you can't even make beer

Minor conjuration works to create a small object. The argument could be made that you couldn't even create a beer in the first place since it doesn't really meet the definition of a single discreet object. See this question (among others) for examples of this argument more in depth.

Assuming your DM agrees, then you can't create beer in the first place.

But even if they do rule that beer can be created, it still wouldn't work to get you drunk.

The beer would disappear upon being drunk

The rest of this answer assumes that your DM allows you to create beer with Minor Conjuration for whatever reason.

Unfortunately, drinking the beer would likely count as damaging it, so the beer would instantly vanish upon the attempt. Not to dive too deeply, but digestion is a destructive process. As soon as the beer enters the body it starts getting broken down by various processes and chemicals in the body. In short, beer doesn't stay beer long once ingested.

Think of it this way, if you took that beer and dipped it into acid, would you count that as damage? I would say yes. Stomach acid does exactly that as part of digestion.

In summary: upon ingestion (or very shortly after) the beer (bottle and liquid) would disappear including the liquid inside the body.

Rules as Fun

I would be tempted to allow a summoned beer to be drunk and for someone to get drunk on summoned beers. However, there is a bit of a problem. If you can summon and drink beer, you can summon and eat food and be sated by it. However, allowing this steps on the toes of other spells and class features designed to do exactly that and at no cost.

This seems unfair, unbalanced, and unfun especially if any characters with those abilities are at the table.

If you don't have an issue with this then there aren't really any further problems with allowing it, but I wouldn't for the above reasons.