Are they made the same way as classical engines ?
They are made quite differently than regular engines that we 'regular folks' have in our cars. Direct quote from http://en.wikipedia.org/wiki/Formula_One_engines :
The power a Formula One engine produces is generated by operating at a very high rotational speed, up to 18,000 revolutions per minute (RPM). This contrasts with road car engines of a similar size which operate safely at typically less than 7,000 rpm. The basic configuration of a naturally aspirated Formula One engine has not been greatly modified since the 1967 Cosworth DFV and the mean effective pressure has stayed at around 14 bar MEP. Until the mid-1980s Formula One engines were limited to around 12,000 rpm due to the traditional metal valve springs used inside the engine to close the valves. The speed required to operate the engine valves at a higher RPM is much greater than the metal valve springs can achieve and they were replaced by pneumatic valve springs introduced by Renault. Since the 1990s, all Formula One engine manufacturers now use pneumatic valve springs with the pressurised air allowing engines to reach speeds of nearly 20,000 rpm.
The bore is the diameter of the cylinder in the engine block, and the stroke is the distance the piston travels from top dead-centre (TDC) to bottom dead-centre (BDC) inside the cylinder. To operate at high engine speeds the stroke must be relatively short to prevent catastrophic failure, usually connecting rod failure as they are under very large stresses at these speeds. Having a short stroke means that a relatively large bore is required to make the 2.4 litre displacement. This results in a less efficient combustion stroke, especially at lower RPM. The stroke of a Formula One engine is approximately 39.7 mm (1.56 in), less than half as long as the bore is wide (98.0 mm) producing an over-square configuration.
In addition to the use of pneumatic valve springs a Formula One engine's high RPM output has been made possible due to advances in metallurgy and design allowing lighter pistons and connecting rods to withstand the accelerations necessary to attain such high speeds, also by narrowing the connecting rod ends allowing for narrower main bearings. This allows for higher RPM with less bearing-damaging heat build-up. For each stroke, the piston goes from a null speed, to almost two times the mean speed, (approx. 40 m/s) then back to zero. This will occur 4 times for each of the 4 strokes in the cycle. Maximum piston acceleration occurs at mid‑stroke and is in the region of 95,000 m/s2, about 10,000 times standard gravity or 10,000 g.
Slightly simpler answer: the more volume of air/fuel you can burn (all around 13:1 air/fuel ratio) the more power you can produce. You can increase the static displacement (e.g. 3.7L V6 vs 2.5L four) or the engine speed. Formula One has always had restrictions on displacement, which required increasing the engine speed or increasing efficiency.
Formula One engines are always accelerating, which makes rotational inertia a concern. The less the better. However, reducing the mass also reduces the strength.
The limitations on engine speed come from friction which increases with engine speed and material strength. There have been street engines with relatively long strokes that could hit 9000 rpms: Honda S2000, Ferrari 458. Both had strokes over 3". However, in F1 the move to small bearings for reduced friction and less mass in connecting rods, crankshafts, piston pins, etc. for less inertia can make failure an issue. Metal valve springs are also subject to failure; racers frequently change them. F1 went to pneumatic valve springs a while ago. Valve stems can have strength issues. They are reduced in size for both less mass and less interference in the airflow.
F1 engines had gotten over 19000 rpms and were approaching 20k rpms years ago. F To reduce costs and increase competition the rules were changed to set an speed limit (19k in 2007, 18k in 2009) and limited the driver to 8 sealed engines for the season. There are also restrictions on bore size and materials used.
The result has been a dramatic increase in engine reliability, although there are failures because of the 8 engine rule.
Note: if rotational inertia wasn't a problem, it would be fairly simple to make an engine with components that could withstand the forces at 18k. However, when you want to minimize friction, minimize inertia, and maximize airflow the issues begin.