1. No .. Cr@p in = Cr@p out.
2. Yes .. buy a Mast amp 2, 3 or 4-way and power supply.
3. Above assuming current antenna is up to the job and correctly aligned.
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Triax or Labgear are best. Don't go higher than around 16dB gain.
Any aerial will pick up both analogue and digital.
But digital does tend to require a roof-mounted high-gain aerial.
To split the signal from the aerial to a number of rooms you need a amplifier fitted near the aerial and the various cables run down from the chmney to each room. I have this in my house, the one aerial feeds into 4 rooms.
Any decent aerial fitter will be able to fit an amplifier for you.