Hi answers to questions below:
1. Will I have any relevant SEO problem to do 301 redirects from the old links to the new?
- If you using 301 redirects to new URLs you should not have any issues, its time consuming and no easy work around since you need to point old urls to new ones but definitely wont loose any rankings.
2. Should I do it all at the same time or do it by parts?
- If you are changing all the urls then do it at once.
3. What options do I have to avoid give not found errors / redirects for the old links?
- Use webmaster tools to assist you with not found errors. I have switched from a static html php site to Wordpress about 2 years ago with approx 2000 pages indexed. Im still receiving not found errors therefore its a good idea to monitor this daily and fix asap.