I want to know how in practice we can take a kHz/MHz signal to a GHz band?
You guessed right: a mixer.
Should I build an oscillator with a frequency of 3499700 kHz (or 3480 MHz) to use it as a mixer?
Assuming these frequencies are the difference between your source and your target frequencies, yes.
But you don't use an oscillator as a mixer, you use its output to feed it to a mixer.
Is it possible in practice to have a precise 3499700 kHz oscillator?
Precise is a relative term. If you build a house, your standard of length needs to be accurate to say 0.2 % (so that if your house is 10m long, its length error will be no more than 2cm). If you build an aircraft engine, you might want to be better.
With oscillators it's usually way, way more precise than that, even on cheap standards.
Technologically, RF devices typically use synthesizers to generate local oscillator (LO) frequencies from a reference oscillator, which might be running, for example, at 10 MHz. A synthesizer typically contains all the parts necessary to derive that frequency – a control loop for a voltage-controlled oscillator, that oscillator, some sort of frequency multiplier, filtering to actually get the multiple you want, control and compensation circuitry…
The precision and stability (two different things!) of the resulting oscillator usually mainly depends on the precision and stability of the 10 MHz reference, and to a smaller extent (at least in the frequency regions you mention) on the noise and precision of the control loops.
Is there any IC useful or should it be by PLL?
This question makes no sense. All the ICs that might make sense here contain at least one form or another of a PLL.
Is there any other and better solution?
You seem to want a mixer + filters + a synthesizer. Mixers and filters can be bought as modules for moderate prices (e.g. from minicircuits), synthesizers often either take the shape of signal generators in laboratory settings, or as synthesizer ICs + support circuitry in actual devices.