A friend who holds an italian passport but he is originally from Venezuela. He has is 5 years old daughter in Venezuela but he is not officially married with the mother. He wants them to get them in belgium where he lives now. They can come with tourist visa. Can they get married in belgium with tourist visa?
Yes, they can get married in Belgium. The requirement for non-Belgians to marry in Belgium seems to be that at least one partner be domiciled in Belgium for at least three months.
It is not necessary for them to marry for the non-Italian partner to stay in Belgium. EU free movement law recognizes unmarried "partners in a durable relationship, duly attested" as qualifying family members. See, for example, the relevant page from Brussels: Relative of a subject of the EU, EEA or Switzerland ("subject" should be "national," but otherwise it's pretty clear):
Partner of a subject of the EU, EEA or Switzerland in the context of a long-term relationship. Please note: both spouses or partners must at least be 21
However, it should be noted that providing evidence of marriage should be as simple as presenting the marriage certificate, especially if the marriage takes place in Belgium. By contrast, proving their unregistered partnership will could require evidence of cohabitation, evidence that they are both parents of the child, and other less clear-cut evidence.
The rights of a spouse also accrue more automatically, since they do not depend on the "due attestation" of the relationship. By contrast, as an unmarried unregistered partner, the rights do not need to be recognized until the proof of the relationship is submitted and accepted. So getting married, while not necessary for the partner to be able to stay, might still simplify the process somewhat.
The daughter is probably an Italian citizen, in which case they should get her an Italian passport.
Long stay visa applications (more than 90 days) or short stay visa applications aiming at a longer stay in Belgium (e.g. marriage in Belgium)
Your friend's fiance will need to get a marriage visa.
More precisely, she can travel to Belgium on a tourist visa, get married, and then return to Venezuela. If she travels to Belgium on a tourist visa, and then doesn't leave (because she has got married), she has lied on her application for the tourist visa - and that can lead to all sorts of complications in future.
However, there is an alternative route. If she can show she is in an enduring relationship with your friend (and the child plus intent to marry is pretty good evidence of that), your friend can use his freedom of movement rights to bring his third country partner to Belgium.