In p. 9, they give a schematic of the way to mount the amplifier (I believe). But at the end of the same page, they specify that pins 1, 10, and 5, 6 require a bias network. Do they mean the 10 Ohm and 10 uF cap in the schematic, or is it something else?
No. 10 μF caps are for decoupling, 10 Ω resistors are for dampening because you are dealing with RF so the parasitic inductance of the supply rail traces will come into play. For biasing, follow the guidelines given in the datasheet. You'll need to make those adjustments for every single board having that Qorvo chip.
They do not specify what kind of resistor and cap is needed. Does it mean that any surface mount resistor and cap could do? if not, how should I choose these components?
For the decoupling/dampening network, any ordinary capacitor and resistor would do. But since this is an RF application, you may also want to use pF and nF capacitors (e.g. 100p, 1n, etc). For them, SLCCs (single-layer ceramic cap) instead of MLCCs would suit better as they are generally designed for microwave and RF applications.
I don't understand the way they write the dimensions in p. 12: what does mean, for example, 4x 0.126 ?
They gave only one dimension to keep the diagram simpler and neater, but they mean "there's 4 of this dimension" meaning that the design is symmetrical.
Same applies to pin dimension as well. For example, RFIN and RFOUT pins are identical (mechanically), so only for one of them the dimension is given.
p. 11 : they say "The leads should be soldered in a staggered or star pattern from side to side". What does that mean (I understand what is a star pattern, but how is it relevant here) ?
Heat dissipation and minimal temperature rise. If you solder the pins on one side first there may be thermal hotspots on that region. Likewise, if you solder all the pins at the same time, the entire thing may warm up quickly. That's probably why they don't recommend reflow soldering. As far as I understand, they recommend soldering one pin at a time, and on the opposite side and with some cooldown time in between.
p. 12. I don't really understand how to mount the amplifier on the heatsink: the amplifier seems to have a basis with some width, and the leads are above the basis. So, the only way I can understand that is that the width of the PCB board is exactly the same as that of the amplifier basis, and the PCB has a square hole into which the amplifier is inserted. Then the heat sink is just under the basis of the amplifier, at the same level as the bottom of the PCB. But I would like a confirmation.
Correct. The PCB should have a thickness of ~1.4mm and a hole for the whole component, so a heatsink can be mounted from bottom.