#3 Most goals in a single game (7)
Agustin Sauto Arana and Laszlo Kubala are the joint holders of this record. Bata, as Agustin Arana was popularly known, scored the 7 goals in Athletic Bilbao's 12-1 win over Barcelona on 18 February 1931. It was indeed a historic game. The prolific goalscorer won 4 LaLiga titles and 3 Copa del Rey titles with Bilbao.
Arana's record stood for almost 20 years before Kubala -- then playing for FC Barcelona -- scored seven goals against Sporting de Gijón in their 9-0 win. He had an impressive 14 hattricks with the Catalans. In all, the potent forward won 4 LaLiga titles, 5Copa del Generalísimo titles, and had a highly impressive career.
#2 Most consecutive league games without a loss at home (121)
This record is held by none other than Real Madrid -- the most successful team in LaLiga history. They went over 8 years (from 17 February 1957 to 7 March 1965) or 121 matches in the LaLiga without losing a game at home. Los Blancos dominated the LaLiga from 1950 till 1980 -- winning the title 18 times.
No wonder the record has stood for over 65 years. All the clubs playing in the top division are so competitive now that there are very few teams who can even manage to go undefeated in a single season -- even at home.