Hi, as for 1st question,
class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.conv1 = nn.Conv2d(in_channels=1, out_channels=10,
                               kernel_size=5,
                               stride=1)
        self.conv2 = nn.Conv2d(10, 20, kernel_size=5)
        self.conv2_bn = nn.BatchNorm2d(20)
        self.dense1 = nn.Linear(in_features=320, out_features=50)
        self.dense1_bn = nn.BatchNorm1d(50)
        self.dense2 = nn.Linear(50, 10)

    def forward(self, x):
        x = F.relu(F.max_pool2d(self.conv1(x), 2))
        x = F.relu(F.max_pool2d(self.conv2_bn(self.conv2(x)), 2))
        x = x.view(-1, 320) #reshape
        x = F.relu(self.dense1_bn(self.dense1(x)))
        x = F.relu(self.dense2(x))
        return F.log_softmax(x)

worked.