You certainly do not need to cover those tattoos up. Lots of Berber women in more residential Tunisian parts have 'inkings' on their faces however, some Muslim believers would consider this Haram.. As a tourist you will be fine.
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Part of dressing modestly in Morocco also includes avoiding any flashy jewellery, accessories, brand names and electronics. You should also cover any offensive tattoos. Women aren't required to cover their head, however you will need to when visiting mosques.
No, you have no right to live with her or to rent a hotel room with her, unless you're married, it is illegal. However, not everybody respect the law in Tunisia, so technically you can't but in reality it is possible.
You're not expected to cover your head, even in towns where the majority of women do so. Most of the beaches you visit will have both Tunisians and tourists wearing a variety of swimwear.
Unless things have changed in the last 3 years, Tunisian are very relaxed about smoking, you could smoke inside, smoke in various places in airport. I remember sitting with a security officer at Tunis Airport havin a smoke in a cafe.