Linear mixed model fit by REML. ttests use Satterthwaite's method ['lmerModLmerTest']
Formula: score ~ group * condition + (1  subject) + (1  token_set)
Data: EN_JT_1
REML criterion at convergence: 512.7
Scaled residuals:
Min 1Q Median 3Q Max
3.2745 0.3231 0.1870 0.6697 1.8834
Random effects:
Groups Name Variance Std.Dev.
subject (Intercept) 0.021850 0.14782
token_set (Intercept) 0.003202 0.05658
Residual 0.091070 0.30178
Number of obs: 852, groups: subject, 71; token_set, 24
Fixed effects:
Estimate Std. Error df t value Pr(>t)
(Intercept) 1.00047 0.03727 85.51605 26.844 < 2e16 ***
groupHS 0.06865 0.05296 106.58618 1.296 0.19773
groupSB 0.03172 0.05862 106.58450 0.541 0.58959
conditionENGJTRRES 0.28400 0.03813 48.55384 7.449 1.42e09 ***
groupHS:conditionENGJTRRES 0.08721 0.04796 756.84544 1.818 0.06938 .
groupSB:conditionENGJTRRES 0.14858 0.05308 756.82431 2.799 0.00525 **

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Correlation of Fixed Effects:
(Intr) gropHS gropSB cENGJ gHS:EN
groupHS 0.569
groupSB 0.514 0.361
cENGJTRR 0.512 0.228 0.206
gHS:ENGJT 0.257 0.453 0.164 0.503
gSB:ENGJT 0.233 0.164 0.453 0.455 0.361
I have run the mixedmodel above, where I crossed two fixed variables (group and condition) with each other to look for any effects of each as well as any interactions between the two.
I have three groups (EN, HS, and SB) and two conditions (ENGJTRRES and ENGJTRGAP).
I have two questions:

I'm not sure how to understand the output under "Fixed Effects"  specifically the final two rows. I believe in the three rows below (Intercept) each group or condition is compared to the reference group or condition: in other words, in the second row HS is compared to EN, in the third row SB is compared to EN, and in the fourth row ENGJTRRES is compared to ENGJTRGAP. Is that correct? I'm not sure about the last two rows. What is being compared to what?

How do I run a posthoc test that will compare all groups and all conditions with each other, as well as show all interactions? I found a line of code here that will let me run a Tukey test for groups, and a separate one for conditions (see below), but I'm not sure how I can run a Tukey test to show interactions.
> summary(glht(model_1, linfct = mcp(group = "Tukey")), test = adjusted("holm"))
Simultaneous Tests for General Linear Hypotheses
Multiple Comparisons of Means: Tukey Contrasts
Fit: lmer(formula = score ~ group * condition + (1  subject) + (1 
token_set), data = EN_JT_1)
Linear Hypotheses:
Estimate Std. Error z value Pr(>z)
HS  EN == 0 0.06865 0.05296 1.296 0.585
SB  EN == 0 0.03172 0.05862 0.541 1.000
SB  HS == 0 0.03693 0.06322 0.584 1.000
(Adjusted p values reported  holm method)
> summary(glht(model_1, linfct = mcp(condition = "Tukey")), test = adjusted("holm"))
Simultaneous Tests for General Linear Hypotheses
Multiple Comparisons of Means: Tukey Contrasts
Fit: lmer(formula = score ~ group * condition + (1  subject) + (1 
token_set), data = EN_JT_1)
Linear Hypotheses:
Estimate Std. Error z value Pr(>z)
ENGJTRRES  ENGJTRGAP == 0 0.28400 0.03813 7.449 9.41e14 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
(Adjusted p values reported  holm method)