repeated measurements of continuous predictors and continuous response variable
(a) should I use lmer routine?
Yes
If so, is it sufficient to call it as lmer(y ~ x1+x2+x3 + (1|Id)?
As a start
(b) How can I apply Friedman's ?Multivariate Adaptive Regression Splines? to such problems? That is I'm looking for an R package solving such problems.
Consider GAMMs eg library(mgcv) gamm( y ~ te(x1,x2,x3), list(Id=~1))