In Mass Effect 3, I did not get a choice of game mode; is it because I imported a ME2 character?

If you import an ME2 character you automatically use the roleplaying mode (the one with combat and dialog choices), only if you create a new character do you get the choice in the beginning. The roleplaying mode is the one closest to how the previous Mass Effect games worked, so the game assumes that players that import a character would like to play that mode.

There aren't really game modes per-se. Rather, they are just presets for two settings: "Combat Difficulty" and "Conversation Mode".

• Action: No Decisions, Normal Difficulty
• Role Playing: Full Decisions, Normal Difficulty
• Story: Full Decisions, Narrative Difficulty

The default for an imported character is Role Playing. However, you can change both these options at any time from the "Narrative" and "Gameplay" sections of the options menu.

Note that if you want to get the Insanity achievement, you will have to use the options menu to change the difficulty to Insanity before leaving Earth.