I had the exact same problem, and saw it through to resolution, so I'm happy to explain the problem and solution in detail.

Without Involving a VPN

It is important to understand the configuration that is required in order to meet your requirements without involving a VPN. Also, this information assumes that no software firewall is interfering, neither on the host nor the guest.

Without a VPN, this is normally solved by creating two network adapters in the virtual machine's configuration.

The first adapter must be set to NAT mode, which enables the guest to access network resources (including the Internet) through the host's network interface.

The second adapter must be set to Host-only, which enables bidirectional communication between the host and the guest.

This adapter is slightly more complex to setup than the first, because it requires modifying VirtualBox's global networking preferences in order to configure the host-only adapter (note: this requires Administrator privileges).

In VirtualBox, go to File -> Preferences -> Network. Click the Host-only Networks tab and click the little + icon to add a new adapter. You will be prompted to elevate VirtualBox's permissions.

Filling-out the Adapter tab is mandatory; it should look something like this (ignore the adapter labeled #2; that's used for something unrelated):

The values on the DHCP server tab are optional. If you're intending to hard-code the IP address for this adapter within the guest's networking configuration, then these values are unnecessary. If, on the other hand, you intend to use DHCP, the values might look something like this:

The last step with regard to configuring VirtualBox is to go back into the VM's network configuration and add the second adapter, which references the host-only adapter that we just created:

Now, in the guest operating system, the network must be configured to utilize these two network interfaces.

On Debian or Ubuntu GNU/Linux, the configuration is as simple as modifying /etc/network/interfaces to look like this:

# This file describes the network interfaces available on your system
# and how to activate them. For more information, see interfaces(5).

# The loopback network interface
auto lo
iface lo inet loopback

# The primary network interface
auto eth0
iface eth0 inet dhcp

# The secondary network interface
auto eth1
iface eth1 inet static
     address 192.168.56.101
     netmask 255.255.255.0

(the purist may prefer to utilize the /etc/network/interfaces.d directory instead, but that's beyond the scope of this explanation)

Restart the guest's networking services, or more simply, restart the entire guest VM, and everything should "just work".

At this point, one should be able to ping the guest VM at 192.168.56.101 and receive a reply (provided a software firewall is not interfering).

Likewise, one should be able to ping the host at 10.0.2.2. This IP address seems to be "hard-coded" into VirtualBox's NAT implementation, or at least specified via some non-obvious configuration directive, and there is little information available as to its origin. But, alas, "it just works".

Given this configuration, all three conditions outlined in your question are met.