Though status says it is synced and mining, I consequently get these:
Does it mean my entries to the lottery are invalid and therefore doesn't have a chance in hitting the jackpot?
Are you staying up to date with a block explorer or pool in terms of block height? Did you upgrade on latest hardfork?
Yes and yes (v0.6.1.1).
It syncs and mines all right (so it seems) but I just get these messages in red. Perhaps these screenshots (from two different machines) tell a better story:
