Grandmasters are financially incentivized to play in GM-norm invitational tournaments. The incentive can take different forms depending on the organisers' choice.
Most often, GM are invited (travel, hotel and meals paid, with no fee asked for playing) and they compete for the money prizes in the tournament (usually the top 3 out of 10 players get money prizes). So at the very very least that week doesn't cost them anything, and they may come home with a few thousands euros or dollars.
In this version they tend to play their best to maximize their money prize.
In some other events they are actually paid to play, but money prizes are low. In that case their incitations to do their most are mostly rating points, fighting spirit and love of the game. Many grandmasters are great fighters even in those circumstances, but some tournaments have the reputation of being "good places" to achieve IM- or GM- norms, because the grandmasters there are less motivated to do their best...
About playing style and draw offers, each player has their own habits. Some tournaments don't allow draw offers at all. Note that achieving a norm usually requires 6/9 or 6.5/9 (+3 or +4), so the "perfect plan" of three draws against GM and 5/6 against fellow candidates is not easily achieved. As often as not, a draw won't be enough and you will need a win against a GM, so you might prefer to face a "fighter" who tries to beat you and gives you chances than a non-ambitious, super-solid opponent aiming for a draw.