Is it Haram to make websites for Businesses which:
a) Have some Haram elements, like the restaurant for example?
b) Are Halal in itself but involve specific issues, like a male dealing with photos of female models in the makeup artist example?

In the name of Allah, the most Beneficent, the most Merciful.

Answer

Regarding your first question, it will not be permissible to design websites for restaurants owned by Muslims who will be selling alcohol and also advertising for them alcoholic products on the website.

Saaiduna Anas Radiallahu Anhu narrates that the Prophet of Allah said, ‘Allah’s curse falls on ten groups of people who deal with alcohol.  The one who distils it, the one for whom it has been distilled, the one who drinks it, the one who transports it, the one to who it has been brought, the one whom serves it, the one who sells it, the one who utilises money from it, the one who buys it and the one who buys it for someone else’. (Sunan Ibn Majah p.242 v.2)

Allah (SWA) in the Holy Quran has said:

“Do not assist in each other in sin and transgression.” (Surah Maaidah v.2)

The answer to your second question is also impermissible in particular if you are asked to put pictures of models on the website you are designing for them.

Only Allah Knows Best

Mohammed Tosir Miah

Darul Ifta Birmingham