What's the best and least expensive way to book a package with hotel and tickets?
Book direct with Disney either online or by phone, this thread will explain all you need to know about booking
https://www.disboards.com/threads/how-to-book-direct-with-disney-room-and-tickets-package.3735087/
I am staying three nights. Do I have to have 4 days of park tickets with a package?
Yes hotel and ark tickets packages are standard when you book direct with Disney. You will get park tickets for your arrival day and departure day and all days in between
Arrival day - park ticket
Night 1
Full Day - park ticket
Night 2
Full Day - park ticket
Night 3
Departure Day - park ticket
Is it better to book hotel and purchase tickets seperately?
No it is not better to book hotel and purchase tickets separately.
Disneyland Paris only really allows AP holders to book hotel room , no park tickets.
You can only get room only at Disneyland Paris through 3rd party sites like Expedia
Then you have to buy park tickets separately.
The separate cost of room only and tickets only often works out more expensive then the hotel and tickets package direct from Disney.
Should I be looking for half board or paying for all meals out of pocket?
That depends. The dining plans at Disneyland Paris can be very restrictive for some people. The Disneyland Dining vouchers are only accepted at Disney owned restaurants. Places like Planet Hollywood and Rainforest Cafe in Disney Village do not accept the Disney Dining Vouchers.
The restaurants in the parks, other than the buffets, have a set menu for the Disney Dining Vouchers. You can order from the Al A Carte menu but you will have to add money. Also many people find they do not use all the Disney Dining Vouchers and thats lost money as Disney does not refund. People find that they choose restaurants based on what is covered by their Disney Dining Vouchers instead of choosing restaurants based on the type of food they like to eat.
How soon in advance should I book? I'm looking at August next year.
That depends, you should check the various different country websites and when you find a price / deal / offer that suits you, book it.
Do I prebook fastpasses or dining reservations or is it more like Disneyland in California where you can do these things same day?
There is a paid Fastpass option which most people find is not necessary. The Fastpass system is the lagcy paper system, the same as in Disneyland California. There are far less rides on the Fastpass system in Disneyland Paris compared to the America parks.
Dining reservations open officially 60 days in advance. However there is alo an online booking option on some countries websites.
It is advisable to book restaurants in advance, as you are planning on August which is peak holiday time in Europe. The table service restaurants such as Captain Jacks and Walts and the character dining book out fast, the buffets not as fast.