I've always kept at least one Gandalf Card with each sphere. Today, I purchased Journey to Rhosgobel and see only three Radagast cards. Not sure why only three and not four, one per sphere... Am I not placing these neutral cards correctly? Are they supposed to be kept separate from all the other influences and shuffled in randomly at will?

The rules for tournament deck building and customization explicitly state that "no more than three copies of any card, by title, can be included in a player's deck" (see rulebook p. 27). In contrast with the 30-card starter decks found in the Core set, "tournament-legal" decks must contain a minimum of 50 cards (with a maximum of three copies of any card per deck… even though the Core set does not give you three copies of each player card). Even when just playing home games, many players choose to restrict their decks to 50 cards.

Adventure packs are sold with 3 copies of each player card, so that a single player can include the maximum number of a particular card in his/her deck (evidently, you might need to purchase more copies of the AP if you are planning to build decks for multiple players, and if several of those players want 3x copies of a particular card in their respective decks… you could always proxy or copy/sleeve copies of cards if you don't want to purchase several copies of an AP just for a handful of extra cards that may or may not see heavy use).

Neutral cards are shuffled in a player's deck the same way other cards are. The only thing that sets Neutral cards apart from cards from other spheres is that any/all heroes you control can contribute to the "purchase" of Neutral cards without requiring a Resource Match (see p. 12). I am not 100% sure what you mean by "placing neutral cards correctly" (the only time you "place" a card is when you play it from your hand to the table), or by keeping Neutral cards "separate from all the other influences and shuffled in randomly at will"… but I think I may have answered your question all the same (it seems that you may have misunderstood some of the rules of the game).

There is only one copy of Gandalf per deck in the Core set starter decks because… that's just the way FFG designed the starter decks! When I play 2-handed or with a second player, it is common for each to have 3 copies of Gandalf in their 50-card decks… you'll find Gandalf x3 in many of the decks posted in the Strategy and Deckbuilding section of these boards. To do that, you either need to buy multiple Core sets, buy singles of the cards that you want in triplicate (from eBay or elsewhere), or either proxy or copy/sleeve extras.

By the way, nothing stops you from reconfiguring the Core set decks to improve their optimization. For example, you could have a dual-sphere deck featuring Leadership and Spirit heroes and cards (+ Neutral cards), and another featuring Tactics and Lore heroes and cards (+ Neutral cards)… or any combination of spheres, really. Tri-sphere decks are also common. The only thing you need to remember when building dual- or tri-sphere decks is that you must have a resource match in order to play a particular card from your hand (e.g., Leadership heroes can only pay for Leadership and Neutral cards, even if you have cards from other spheres in your deck. Playing a card like Celebrian's Stone on Aragorn allows him to pay for Spirit cards as well).

I hope that helps.

It does, thank you!