The given first reaction is an example of E2 elimination.
E2 elimination:
In E2 elimination proton, abstraction by the base and leaving group leaving will happen simultaneously. Primary and secondary substituted carbon with strong base favours the E2 elimination.
The false statement is the reaction is under kinetic control.
In the given second reaction also example of E2 elimination.
In sodium, methoxide is the strong and small base so which will give the more substituted alkene is the major product. So the first statement is true. If we use a bulky base then we will get less substituted alkene as the product.
Kinetic control gives less substitute product so the second statement is false.
Thermodynamically control gives more stable more substituted alkene is the product. So this statement is true
According to Zaitsev rule, more-substituted alkene will form in the elimination product. So this statement also true
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