First of all i’d like to say I got this game yesterday and i’m loving it, really fun.
Alchohol Abuse and Internet crime are 2 problems i’ve been stuck with and can’t seem to get rid of. I’ve cranked Policing, Community Policing, and Intelligence Services up to full but I still cannot abolish these 2 problems.
Has anyone here recovered from these problems? I don’t want to tax alchohol or put internet censorship on if that helps.
I got rid of those problems yesterday and I taxed alchohol and put internet censorship 
I remember my alchohol restriction age 21, alchohol tax over 50% and it took few turns to abolish alchohol abuse.
For the Internet crime, I first killed crime rate to zero, with help of other policies.
and then I began to censor internet, it just disappeared.
probably you’ll say this sounds like too socialist, but I solved problems and I liked it 
hope you find your own way
Nah, I like socialism. I just don’t want it to seem too totalitarian.
If you do not want to restrict Alcohol law or Tax it , then you need to address it indirectly (whether this will be enough is another issue). Large sections of society do not change their behaviour on a whim, they have to “encouraged”. However if you have done something very liberal like NO DRINKING AGE, then IMO you will never be able to do enough to resolve it, your policies are creating the problem. There is no such thing as a completely unrestricted society without issues
Address the other potential sources of DRINKING ie POVERTY, UNEMPLOYMENT, OTHER SITUATIONS like HOMELESSNESS, etc. Potentially add in new POLICIES that MAY affect it, ie YOUTH CLUBS might discourage DRINKING (don’t know, just spitballing here).
Hope this helps, but it kinda sounds like you are aiming for is akin to wanting to legalize drugs and then get rid of an addiction epidemic, or like trying to adequately defend a country whilst dismantling the military. Only so much can be done.
BTW Not judging your choices here from an ideological perspective, solely a gameplay one.