Secret doors: if players specifically mention they search for one in a specific area where there is one, such as under the carpet or behind the cabinet, they find it, no roll. If they quicly sweep through a room or a corridor without any specific indication as to their search, not thinking of finding anything but thinking there might be the odd chance of a secret door there, then I roll a search die with a DC. Elves and thieves get d20 (trained), others are likely to get d10 unless their background somehow allows them to be trained. Intelligence is the key attribute for me on searching. DC depends on the secret door. DC 20 would be a very well crafted door on a masonry stone wall, e.g. of dwarven craftmanship. DC 10 would be the removable wooden panel in a peasant's hut.
Surprise: I just about never roll for surprise. In fact, I can't remember having rolled for surprise. If PCs and monsters fall on each other without expecting it, they are both surprised, and we roll for init as usual. If both are wary and fall on each other and expecting it, neither are surprised, and we roll init as usual. If one group is stealthy and wishes to creep up on the other, then I will have a single group stealth roll (the one among move silently and hide in shadows that seems most appropriate if the thief is the determining character) opposed by a single group perception roll by the other party. If it succeeds, there is suprise; otherwise, not. If the entire party is moving "stealthily" with armored characters, the group stealth roll will incur a significant penalty. I wing it depending on the conditions (silence, night time, grass or stone underfoot, etc...)