No. Tipping is not mandatory. If service was exceptional, rounding up or leaving 5-10% is appreciated but certainly not expected.

Can I get a doggy bag?

It is very uncommon in Italy. Portion sizes are usually balanced, and taking food home is often seen as strange. Try to order only what you can finish.

Dining in Italy: Understanding Meal Times and Customs

In Italy, dining follows a strict, slow-paced schedule where lunch happens between 1:00 PM and 2:30 PM, and dinner starts no earlier than 7:30 PM. Understand that restaurants are rarely open for service between meals, and you are expected to sit for at least an hour to fully enjoy your food and service.

Respect the 'orario'. Most restaurants close their kitchens between 3:00 PM and 7:00 PM. If you show up at 4:00 PM, you will likely only find bars serving small snacks or paninis; do not expect a hot meal.
Master the flow of the meal. An authentic Italian meal is ordered in stages: Antipasto (starter), Primo (pasta/rice/soup), Secondo (meat/fish), and Dolce (dessert). You do not need to order all of these, but never mix pasta with a meat dish on the same plate.
Handle the bill (Il Conto). Servers will not bring the bill until you ask for it. Catch their eye and say, 'Il conto, per favore.' They will not rush you out, as the table is yours for the entire evening.
Coffee etiquette. Order your cappuccino only in the morning. After 11:00 AM, Italians switch to an espresso (caffè) because milk is considered too heavy for digestion following a meal.

Do I need to tip?: No. Tipping is not mandatory. If service was exceptional, rounding up or leaving 5-10% is appreciated but certainly not expected.
Can I get a doggy bag?: It is very uncommon in Italy. Portion sizes are usually balanced, and taking food home is often seen as strange. Try to order only what you can finish.