As others have said, very close. However, rather than approaching it from the centre of Valletta, the simplest is to enter the city via the main gate, walk straight down Republic street about 100m before turning right (Triq id Nofsinhar), past Piazza Jean de Valette and taking Castille street (off Castille Place) to arrive at the Upper Barrakka gardens (5-10 minutes from the Gate). The view is the main attraction rather than the garden itself.

It depends how long you want to stop. From Upper Barrakka you can admire an amazing view, it could take from 5 min to even half and hour. Lower Barrakka are smaller, maybe you can visit them a bit faster. To go from one to another it takes just 10 minutes of walking.

Se non sbaglio a mezzogiorno...

a) the entrance is free. b) I dont know. c) at noon - 12 am.

It is at the opposite side of Valetta which involves walking uphill and steps or you can walk around the perimeter wall of Valletta

Looks like it's open longer in summer than winter!

Yes you can, but it's a winding route. Go through the short tunnel and follow round to the left to Victoria Gate. Through the gate and turn left up the steps and at the top turn right over the bridge (the Bridge Bar is worth a visit in the evening ; especially Friday evening when there is a jazz band playing during the warmer months). The Grand Harbour Hotel should be in front of you (that's where we always stay) -- go straight up Battery Street and then up the steps, or to the other side of the hotel up the steps of Ursula Street. The gardens are in front of you. The new lift is easier. Nearly 200 feet high with views of the harbour as you go up and it costs just 1 euro each. If you time your arrival right you will catch the noon gun being fired from the Saluting Battery just below the gardens overlooking the harbour.