1. As players sacrifice creatures and discard cards with Death Cloud, Tergrid's triggered ability will trigger each time an opponent of Tergrid's controller discards a permanent card or sacrifices a nontoken permanent this way, even if Tergrid is sacrificed at the same time as the other creatures (C.R. 603.10a, 603.10, 603.6c). However, if Tergrid is sacrificed this way, it won't be on the battlefield anymore when players sacrifice lands with Death Cloud, so that its triggered ability won't trigger for those lands (C.R. 113.6). This is because Death Cloud's instructions are carried out in the order written, not simultaneously (C.R. 608.2c). See also this thread.
2. It depends on how Tergrid's controller chooses. If Tergrid's triggered ability triggers more than once while Death Cloud is resolving, those abilities will all go on the stack at the same time (namely after Death Cloud finishes resolving), and Tergrid's controller chooses the order in which they go on the stack (C.R. 117.3b, 117.5, 603.3b, 116.8). The cards the abilities refer to will then get to enter the battlefield in the reverse order in which the abilities were put on the stack this way (to the extent that player chooses to return those cards this way) (C.R. 405.2, 117.4). See also this thread, this thread, and this thread.
1. Would Tergrid’s controller get all permanent cards sacrificed/discarded from DC; or would the lands be excluded?
2. How do all permanents enter? Do the discarded cards get put in last (compared to the ones sacrificed)?
2. It depends on how Tergrid's controller chooses. If Tergrid's triggered ability triggers more than once while Death Cloud is resolving, those abilities will all go on the stack at the same time (namely after Death Cloud finishes resolving), and Tergrid's controller chooses the order in which they go on the stack (C.R. 117.3b, 117.5, 603.3b, 116.8). The cards the abilities refer to will then get to enter the battlefield in the reverse order in which the abilities were put on the stack this way (to the extent that player chooses to return those cards this way) (C.R. 405.2, 117.4). See also this thread, this thread, and this thread.