1. I think taxi is better since you will travel with luggage and there is no direct bus from Airport to your hotel, about 50MOP;
2. You can walk to Na Tcha Temple from your hotel, then walk to Ruins of St. Paul's, after that you can take Bus 6, 7, 10, 10A, 18, 21 to A-Ma Temple, from A-ma Temple you can take Bus 18 to Macau Tower, and there you can take Bus 32 to Fisherman's Wharf, there you can walk to Sands Macau and take the free shuttle bus to Venetian Macau, from Venetian Macau you can take Bus 25 or 25X back to the hotel.
3. Senado Square is good, Mont Fort is close to the Ruins of St. Paul's. Here are some Macau Hiking Tours(https://www.travelchinaguide.com/tour/hiking/macau/) for your reference.
4. No free shuttle bus from airport to your hotel.