Programs that lead to professional registration tend to be very competitive and are often oversubscribed. The number of places available depends on country and university context and in many cases are set by the state. You can find out more about this by looking at the various report cards on O-Health-Edu or exploring the national level reports.
While in the past this might have been viewed as a challenge, most Universities now have either left handed chairs or chairs that are modifiable to either right- or left-handed practice. So this should not be an issues for you.
The entry requirements can vary from country to country. Generally, you will need to have a high level of academic skills, thus in most countries having the sciences and maths can help you qualify for a place. In many countries entry is through a centralized application system and this may include some form of manual dexterity skills testing however, remember the purpose of your training is to help you gain these so the skills required at entry will be simple. Some university may interview you to assess your communication, empathy competence.
There is currently no centralised system for applications at a European level. Application in on a country by country basis. In many countries there is a centralised application process where you can apply to study in your hierarchy of preference.
In many countries there is a national centralised applications system that allows you rank your preferences, while in others application is direct to each university.
