If you are working in another country, you and your family must be treated exactly the same as your colleagues who are nationals of that country. This applies especially to:
Equal treatment prohibits not only open discrimination, but also any rules that indirectly place you at a disadvantage, such as measures limiting your free movement.
For example, a rule that required you to live in the country for a long time before you could access a particular public service would be illegal.
YES — whatever their nationality (even non-EU), your family members:
NO — not at all. You are subject to temporary restrictions on access to the Austrian job market, but this does not affect any of your rights as an EU citizen, including the right to be treated exactly the same as local workers.
If your employers persist with this attitude, you should report them to the Austrian labour authorities.
If you think that a rule or decision affecting you is against EU rules allowing you to work abroad, you must first take your case to the authorities in the country where you work.
Depending on the exact problem, you might also be able to get help from the EU assistance services.
YES — if he's recognised as having the right to stay with you in Slovakia, he'll enjoy the same rights as you.
YES — under certain circumstances.
If you're living there legally, you're entitled to the same basic welfare assistance — called also social assistance in EU law texts — as nationals of that country. Depending on the country, this may include income support or other benefits that are independent from previous contributions you may have made to the welfare system of that country.
However, your new country may decide to withhold your entitlement to income support — or other benefits — for the first 3 months of your residence (for example if you came as a seasonal worker, worked 1 month and then applied for income support), and for even longer if you arrive in the country as a job-seeker.
Each EU country is obliged to set up a point of single contact to act as a one-stop shop for service providers.
The UK point of single contact will give you all the information you need either to start a new business or to provide cross-border services. It will also enable you to complete — electronically — all the administrative procedures in one go. You won't have to contact all the relevant authorities individually.
If you want to provide cross-border services, you will normally have to deal with less formalities than if you want to set up a business. For example, you should not be required to obtain prior authorisations or to register yourself with UK authorities — this may be required for example in case of environmental concerns, health and safety requirements on the business premises or other procedures linked with the place where the service is provided.
If your profession is regulated in the UK, you may need to get your qualifications recognised by UK authorities. This can also be done via the UK point of single contact.