There are a few errors in Burgerland's post.
1) Luxembourg's labor laws are considered employee friendly, in line with Luxembourg's tradition of closely following French and Belgian laws and jurisprudence. It is way more difficult to get fired in Luxembourg than in Germany, UK, Scandinavia etc.
The minimum notice period is 2 months not 1. Maybe Burgerland meant the severance payment?
The employer can dismiss you but only for a cause. He cannot just dismiss you on a whim. Those causes will be examined by the labor tribunal and if the tribunal doesn't believe the dismissal was justified it can cancel the dismissal and order the employer to pay substantial damages (lost wages + other damages + reimbursement of the court costs).
Reasons for dismissal must be supported by demonstrable and explicit facts. Such facts include: • reasons connected with the employee's aptitude; • reasons connected with the employee's conduct; or • reasons arising from the operating needs of the business, establishment or department. It should be noted at this point that if the employee challenges the reasons indicated, the onus is on the employer to demonstrate that they are well founded.
The procedure in labor courts can be relatively speedy for certain aspects of the case (référé). The court can force for instance the employer to keep paying your salary until the court case has been decided. The union will normally pay your lawyer. Concerning the notice period and severance pay you need to check the cwa and not only the law. You can only get fired without notice and severance for gross misconduct (faute grave). Courts are very strict in examining the alleged gross misconduct. The employer needs to prove his allegations.
Some of the guys from across the street received very substantial damages for unfair dismissal a few years ago.
2) The 52 week period has just been extended.
3) It depends on your doctor's sick note if you are allowed to leave the house only for a short duration or longer periods (sortie autorisée or non-autorisée). It really depends on the nature of your sickness. Obliviously if you are on sick leave with "sortie non-autorisée" you can not do any home improvements, mow the lawn, play sports, go out dinning etc etc. Inspections are in fact very rare.
For more details just google Luxembourg labour law. There are many webpages in English.