What exactly is happening in these models when an intercept is removed from a mixed effects model?

I have the following data:

set.seed(3)

library(data.table)
library(lme4)

a <- rep(1:5, times = 20)
b <- rep(c(1,1,1,1,1,2,2,2,2,2), times = 50)
ppt <- rep(101:110, each = 10)
item <- rep(1:10, times = 10)
dv <- rnorm(n = 100)

contrasts(data$a) = contr.sum(4)

data <- data.table(cbind(ppt, item, a, b, dv))

data$ppt <- as.factor(data$ppt)
data$item <- as.factor(data$item)
data$a <- as.factor(data$a)
data$b <- as.factor(data$b)

I would like to get a coefficient for each level of a. u/omsa_d00d and u/dead-serious pointed me to the idea of running a model without an intercept.

If I run this model:

m1 <- lmer(dv ~ a + b -1 +(1|ppt) + (1|item), data = data)

I get coefficients for each level of a.

However if I run this model in which b comes first:

m2 <- lmer(dv ~ b + a -1 +(1|ppt) + (1|item), data = data)

I get coefficients for each level of b, but not a.

1. What exactly is happening in each case?

2. Additionally, is running m1 sufficient to get an effect of each level of a compared to the grand mean, while also controlling for b?

3. Does it matter if I mean centre my predictors first?

4. What are the different implications of dummy vs. sum coding factor a?