¿What are the main differences betweem communism and socialism?

According to Marx socialism is the next stage, and that stage will lead to another, communism, which will be the last stage of history. When communists talk about state or pretty much anything, they actually talk about how they envision socialism, not communism.

In terms of ideology, socialism is an umbrella term under which various ideologies fall. Communism is one of these, or let's say a subset actually, but not the only one. Originally, communism was designating ideologies close to orthodox Marxism, now it's some kind of umbrella term too.

Sometimes socialism is used to designate democratic socialism or social-democracy, which are opposed to authoritarianism and mostly favor gradual changes over revolutions. Over the time social-democracy came to adopt capitalism as it's mode of production which makes it out of socialism strictly speaking. Some communists adopted gradualist strategies too, and often the difference between all these is better explained by the history of each orga than their positions or ideologies.

3-¿Would a doctor, a scientist or an engineer be part of the proletariat or the bourgeoisie? ¿Or are they from the middle class maybe?

A doctor would be a petty bourgeois if he owns his practice, a prole if he's employed by an institution. The two others are proles.

Proletariat = works for someone

Petty bourgoisie = owns his own means of production

Bourgeoisie = others work for him

4-¿What do you believe education should be like in a communist society? ¿Should it be unified (Teaching the same program for all people) or more specific or specialised (Teaching the subjects the individual is interested on and giving a basic education on the rest)?

I don't think most communist have a clear vision of what education should be in a communist society, when they discuss about education they talk about socialism mostly.

I don't think anyone thinks teaching the exact same program to everyone is a good idea. Socialist formating everyone to be exactly the same is a caricature used by propaganda.

In my vision of socialism education would be mostly handled the same it is today in most countries, entirely or almost entirely run by the state (coops or associations could take care of very specialized needs on the side), but with much more effort to make it easily accessible to everyone. That means free or almost, financial support for students etc. This also means more social security so people can quit one career and learn new skills, as well as continuous education.

I consider easy and equal access to education to be at the center of my brand of socialism.