Italy advise

Generally in this type of trip I would recommend to fly to a northern city (Venice or Milan) and return to SIN from Rome (FCO).
However if you fly Singapore Airlines, I think they fly to Rome only, so the above open jaw option would require a layover somewhere.
If you decide to fly Singapore Airlines in and out of FCO that flight arrives at FCO early morning (7:50am currently), therefore I would recommend you either fly to the furthest point (Venice) upon arrival or take the train (about 4.5 hours trip). There are also 2 trains departing FCO airport station directed to Venice which requires no change at Roma Termini (Rome main station). They depart at 10:08 and 15:08. All other options require a train change at Roma Termini.
Then from Venice you would work your way down back to Rome via train.
The sequence from North to South is:
Venice, Bologna, Florence, Rome.
The train trips from one city to the next ranges from 37 minutes to 92 minutes.
Visiting Rome would be your last stop before coming home.
Whether Bologna can fit in your travel plans depends on the length of your vacation.
I recommend 3 nights for Venice, at least 3 nights for Florence/Tuscany, at least a minimum of 3 nights for Rome. Bologna can be seen in a day, so a night should be sufficient, unless you want to visit it on your way from Venice to Florence, without spending any nights. For example you could leave Venice early, reach Bologna by train in just over one hour, put your luggage at the luggage storage at the station, and after a full day of visiting, retrieve your luggage and travel the last leg from Bologna to Florence (37 min by high speed train).
Since your trip is less than a week long (6 nights on the ground?), unless you can prolong it, you should consider eliminating something, such as Bologna. All you can do is 2 nights in each of the other cities, if you have a 7th night, give 3 to Rome.

That is way too much for 8 days. Bologne should go at minimum but you really don't have time for 3 major cities with so much to do in 8 days. Arrival day and departure day are wasted. I would choose two of these. If you do decide to do 3 then spend 2 nights in Venice and 3 in the other two locations.

As the above suggestion, I would go to either Venice or Florence on arrival in Rome and finish in Rome. That way you use that initial jet lagged day to get to a distant point and you don't waste the day before you fly out rushing back to home base. So arrive in Rome, go to the airport train station and buy tickets to Termini in Rome and to either Venice or Florence. It costs more at the last minute but with such a long flight you don't want to have to worry that if your plane is late, you will miss your train. They will sell you a ticket for a train that you can easily make and by buying it at the airport train station, you will not have to contend with the confusing lines at the main train station.

So head for Florence maybe, spend 3 nights two full days there and then head to Venice and spend two nights which gives you one full day. Of these cities Venice is the one that is most likely to repay such a short trip. Then train back to Rome for the final 3 nights and you have two full days there -- one for the Vatican and one for historic Rome. As you can see this is really not enough time for Florence and Rome each of which is crammed with interesting things to see -- but it makes the trip at least possible. One more stop and you really are doing nothing but moving from place to place.

If it were me I would choose two of the three cities and enjoy some time in each.

What time do you land in Rome on Nov 1? What time is your departure on Nov 8? It will probably take you an hour to get through the airport, maybe less if you only have carry-on luggage. Then it's about an hour to the Rome train station. You'll need time there to buy your ticket to Venice. Trains depart about once an hour to Venice, most take close to 4 hours. So even if you land at noon, you probably won't get to your hotel in Venice until around 7 or 8 p.m.
Nov 1 arrive Venice in the evening (2 nights)
Nov 2 Venice
Nov 3 Venice, evening train to Florence (2 nights)
Nov 4 Florence
Nov 5 Florence, evening train to Rome (3 nights)
Nov 6 Rome
Nov 7 Rome
Nov 8 Rome - pick up luggage at hotel at least 4 hours before flight to Singapore.

Taking evening trains allows you to maximize daylight sightseeing hours. You can have picnic dinners on the train. If your hotel in Venice is far from the train station, you may want to store luggage at the station for the day instead of going back to your hotel - or you may want to spend the 3rd night and take an early train. Transportation within Venice is by vaporetto (water bus) or on foot. Both are pretty slow, so it can take a long time to get from your hotel to the station.

I will arrive rome at 7:15am (1Nov)
Depart Rome at 11:15am (8Nov)

I plan to visit Venice 2day 1 night and spend more time in florence and Rome.